This one's a jungler! I estimated Bloodseeker to fall into the "poor" category - something I would not try in an actual pub game. Let's take a look:
First of all, Bloodseeker is melee - and that's bad news for supports. He is actually kind of unique, primarily due to his third ability Thirst. It gives vision of enemies below half health, and true sight of enemies below a quarter. On top of that, it also gives Bloodseeker bonus movement speed and damage for each enemy below the threshold - and he is allowed to exceed the hard movement speed limit while under effects of Thirst. With Thirst active he is ridiculously good at chasing. Because the vision it grants is global, it always helps your team which makes it an amazing utility ability. It also allows him to hit pretty hard when enemies get low, even if he has no carry items. His first skill is a good silence on early levels or a hefty damage buff at later levels. It's also a decent early game damage over time nuke. Since it's no longer removable, it's a very powerful silence against certain heroes - you just have to be mindful of the damage buff you're giving them with the silence. Early game it really works a lot like Skywrath Mage's Ancient Seal. It's also his carry ability in a sense, but just like Vengeful Spirit's aura, it can just as well buff another carry instead.
So these two skills are not actually that bad for supports. What about the remaining two? Bloodbath has great synergy with Thirst as Bloodseeker regains a substantial chunk of health whenever he finishes off an enemy hero - this means you can dive even under towers and live to tell the tale. If you're a support, then you can feel free to take even more risks. Bloodbath also allows Bloodseeker to jungle, although he is horribly slow at it because he doesn't have any skills to accelerate farming - he can merely survive it (and even that is a bit tricky). However since he is absolutely useless in lane, he should probably be played as a fourth role jungler when played as a support. I seriously do not recommend playing a core Bloodseeker in the jungle, the farm is just way too slow. Finally there's his ultimate Rupture, which is good for making enemies stay where they are. This is obviously a good ganking ultimate, allowing him to show up in a lane and get a kill with his allies. Its cast range of 1000 units makes it really easy to use - and also safe.
As a core Bloodseeker, prioritizing Thirst is the obvious thing to do. If, for some god awful reason, you're lane supporting, I guess you should also go for it. However, in jungle you need to prioritize Bloodbath in the early game in order to sustain your farm. I would not straight out max it, but one level is clearly not sufficient. Even as a support I still think maxing Thirst first is worth it. In the early game it's also usually better to leave Blood Rage at one point to get that sweet 6 second silence without buffing the enemy too much. That is one hell of a value point. Since Thirst level 2 is significantly stronger than level 1, it would be ideal to have 1-2-2-1 by level 6. However at this point I'm not sure if you can jungle with only two levels of Bloodbath. Whether you grab the first point in Thirst level 2 or level 4 depends on the laning situation. If you think you can get a kill with your safe lane on level 2 with Blood Rage, I'd go for that instead of Thirst - but if not, picking Thirst might help your team or help you farm a bit faster while enemies are low.
Here's what you will build: Mekansm. This is going to raise some eyebrows in the pub scene, so let me explain. Mek is often built by the team's jungling support because they can get it with decent timing - this most people know. On the other hand if you look at cores who commonly build a Mek - heroes like Viper, Doom, Razor or even Troll Warlord - there's a clear pattern. All these heroes get their early and mid game damage primarily from their abilities and by staying alive in teamfights. They also aren't particularly mana-starved. Guess what? Bloodseeker fits this pattern perfectly. I realized this when I was watching a replay of my friend's team (shoutout to VSP!) where they pretty much lost because they didn't have a Mek early enough. I think they tried to build it on their offlane Centaur but he also really needs a blink. Since other heroes were not suitable Mek carriers, Bloodseeker would have been the best choice. The more I thought about, the more it made sense too.
Sure, Blade Mail is amazing on him, but if your team needs a Mek and none of the cores are getting it, your jungling support Bloodseeker definitely should. As for other items, well. People usually scoff at Force Staff on Bloodseeker because it's such a quirky build (it makes your ultimate a stronger nuke in a sense but the damage is honestly not that hot). However, as a support, Force Staff provides amazing utility - and since that's what you're here for, its synergy with your ultimate is just a bonus. The 10 intelligence it gives is also enough to solve any remaining mana problems. I don't see any reason to rush a boots upgrade when playing Bloodseeker as a support. That makes my suggested build: brown boots, Mek, Force Staff. After that the build becomes more situational. When you eventually upgrade your boots, I would go for either Power Treads or Phase Boots. Treads are good if you still experience some mana problems, whereas Arcane Boots would be overkill.
I guess you can pretty much build anything in the late game. Diffusal Blade should be good, or you could even go something like straight Hex if you're getting a lot of gold from kills. Maybe even a Rod of Atos so you can prevent two targets from running away - although since he's an agility hero Diffusal is probably better. Blade Mail is also still a very good item (think support Wraith King) because you will become stronger when enemies take damage by hitting you, and can also regain your health when they die. Honestly though, just like a core Bloodseeker, after getting your basic items you can build pretty much anything. Finally a word about starting items. Quelling Blade is a necessity because it's the only way to accelerate your farming speed, and it also makes jungling more sustainable (remember that Bloodseeker only gains health when he kills something). You should not buy wards because you're going to need every bit of gold to stay alive - either grab a Stout Shield or just a bucketload of Tangos.
Get your starting items, grab a level of Bloodbath and head into the jungle. If you're not familiar with chokepoint jungling, you really need to get that shit down to have any chance. You also really need to start by stacking the pull camp once, pulling the creep wave into it and farm the double stack while making sure to deny the entire creep wave. If you are on the Radiant side, you can also try the pull-through into the medium camp instead of stacking the small camp, but it's a lot riskier and you might not be able to clear the camp anyway. I would play it safe because Bloodseeker's jungling is just really weak. Once you hit level 2, take a look at your safe lane or mid. If there's a possibility to get a kill with either Blood Rage or Thirst, try and go for that. Otherwise just keep farming towards your Mek. I would grab boots first though, because they allow you to get kills when there's an opportunity. Getting an early TP scroll is also recommended.
With a level of Thirst, boots and a TP scroll you can easily show up to early fights and secure a kill or two for your team. Don't ever be hesitant to do so, even if you might get killed in the process. If there is no opportunity though, then feel free to use the Thirst bonus damage to accelerate your farm a bit. Once you have your Mek and level 6, you should start putting them to good use by ganking whenever Rupture is up. Since it's not such a long cooldown, and using it along with Mek and Blood Rage blows all your mana, I'd expect you will mostly be ganking and returning to base to regen. Farm the occasional creep where able to work toward your Force Staff but remember that most of the money should come from kills and assists from now on. Since you're the Mek carrier, you should always be with your team when they go for pushes or Rosh.
Don't be greedy with your Force Staff - use it! Always saving it for a Ruptured target is honestly not worth it. Often pushing a Ruptured target also does get them away from your teammates, possibly allowing them to escape. Remember that it's a utility item: you can save your allies or push yourself to initiate from even further with Rupture. Even better, you can pull an enemy into your team when they're facing the right way and then Rupture them to prevent escape. If you really want a nuke, it's probably better to just build a Dagon. A late game Bloodseeker actually has a lot of utility with these items, so you should aim to stay alive in fights. You provide healing, positioning, vision, silence and bonus damage to your carries - just make sure they don't need to use their skills for a while when you buff them! The buff from Blood Rage has particularly strong synergy with stat-based carries - and of course Tiny. Your ultimate also does its damage through BKB, which makes it a strong late game skill.
I actually tried this build twice. First against bots and they got absolutely smashed - they're not very good at playing against Bloodseeker in general I think. Encouraged by this, I actually picked Bloodseeker in a single draft game and went to the jungle. My team had no objections to me building a Mek, so I decided to try this build. The early game, especially between levels 2 and 3, is horrible. I got particularly unlucky both times, as my chokepoint camp spawned centaurs - by far the worst medium camp you can get as a Bloodseeker. I was literally down to dying from one hit multiple times. In the bot game I actually had to even go back to base once to regen. In the pub game I just kinda had to hang out a bit while healing with tangoes. I tried two starting item builds: stout and a pack of tangoes, and just three packs of tangoes - I figured that since I'm mostly chokepoint jungling, the damage block from stout has diminished utility and having more healing might be better - but I'd really need to do the math.
One thing I noticed is that even a level 4 Bloodseeker is surprisingly strong when he shows up to help clean up an early fight. The 120 damage from a 6 second silence is nothing to scoff at, and it often helped in putting targets below the Thirst threshold - and then I just dived them. Yes, with a level 4 support Bloodseeker sporting nothing but brown boots. However if you never get those opportunities, the early game is going to suck - especially if the enemy team has the mind to look for you in your jungle. After getting my Mek at around the 12 minute mark things got a lot easier, and at this point Bloodseeker honestly becomes a perfectly legitimate utility hero. In the pub game I had some good synergy with my teammates as I found it particularly effective to give Sniper some of that sweet bonus damage - we also had a Tiny who ended up hitting buildings for almost 700 damage.
Bloodseeker's biggest weakness as a support hero is his horrible early game. He is often played as a solo mid because he really benefits from having a level advantage. When farming the jungle, his experience gain is diminished severely, unless you get some kills. A 12 minute Mek is also not the fastest, and you might not even get it if you get no kills or get ganked once or twice. However if you make it past the early game, I think he's actually quite strong as an unconventional support. Sure, you cannot solo kill anyone, but if you bring even one ally who has a stun, it's really easy to kill heroes: force them into your ganking squad, use Rupture and possibly silence (or buff your partner) - that's a kill. If you can initiate a teamfight with this combo, you're also off to an amazing start.
My initial ranking for Bloodseeker is clearly off. I think he is at least playable as a support, and perfectly legit if you can get off to a decent start. So if you're ever stuck with four core heroes as a Bloodseeker and head to the jungle, try to play him like a support. Get that Mek, and get those early TP scrolls to show up in lanes and cause trouble! It will be way more fun and useful than afk jungling.