Blademail is actually really legit on BS. If you get it quite early after treads/phase, you rupture someone, drop your silence, bloodrage yourself and run at them. If they're alone, they're fucked.
Only if they are way out of position. By the time you're speaking of "early", you're most likely going to TP out because BS is not going to kill you in 3 seconds that easily. But if you are waaaay out of position, alone, among enemy creeps and on top of that, you're already low HP and have no mana for TP, you're toasted. It's just that good players will not allow this luxury if they're playing against bloodseeker

They'll also ward the shit out of places BS can sneak through.
BS is one of the most obvious punisher heroes in low level pubs due to this - because he exploits a lot of different kinds of mistakes. Overreaching offlaners, people getting beaten by creeps, alone and out of position and mana and tps are all things that often happen in low-coordination pubs, so BS players can easily get away with just locating people and murdering them. Also not calling missing.
Among other things, in noncoordinated pubs it's also easy to have someone pick axe with bloodseeker on the other team, get low health, and screw whoever lanes against bloodseeker or just have bs run up to him to murder him. And naturally, there are no wards so he won't even see it coming. It's just that bloodseeker does well against lack of coordination, much like techies and invisible heroes because unlike majority of heroes that punish one or two specific kinds of mistakes, bloodseeker punishes a wide myriad. But he's just so easily countered that it's ridiculous, hence why him, ursa, riki and similar heroes are so underpicked in the pro scene. You run away from ursa, get a plenty of forcestaffs, buy sentries and blademail against riki, coordinate your positioning and health team-wide by default (teams do this naturally, they don't need bloodseeker to force it), report missing, etc, and those heroes really can't do much, especially considering they are mostly crappy at teamfighting as well.
Positioning is the most important thing in dota, hence why shadowfiend is tier 1 of the past patch's meta - he's ridiculously squishy and can dish out tons of damage. So you don't get him in position to take any, and get him into position to dish tons, and you've won. This is also why vengeful spirit and batrider are tier 1 pick/bans of the previous patch - positioning. She can save whatever squishy carry is shredding the other team to pieces and meanwhile dying, and she can reeeeally punish low mobility low teamfight carries much in the same way as batrider can - this is why carries like riki, bounty and bloodseeker are just not seen as much in the pro scene - they depend on bad positioning of the enemy's team, but to exploit that, they themselves have to get into a really bad non-teamfight position, and that screws them over. Unlike tier 1 carries - juggernaut, sniper and shadowfiend. Jugg can ult without taking absolutely any damage, sniper can dish ridiculous amounts of damage from a position so far nobody can actually reach him if positioned well, shadowfiend has a pretty nifty range, and you don't want to come close to him either, because he's also got spammable nukes that make you not want to walk towards or from him (not to mention his ult), basically, he punishes your change of position.
But all this being said, blademail is really good item on bloodseeker. If you are raged and try to fight back you are actually double screwed - you get bonus damage to deal to bs, and then BS deals that damage back to you as pure damage (of course, after magical damage reduction/armor, but you also take % damage more). If both you and you and BS are raged, however, you get a funny situation - you deal 40% more damage, while he takes 40% more damage, then his blademail turns this damage back to you, but since seeker is also raged, it deals 40% more damage, but don't forget you also happen to take... 40% more damage. So if you attack a raged bloodseeker while you're also raged, you will receive 100%*1.4*1.4*1.4 = 275% of your own damage (before reductions, mind you, as seeker's armor and magical damage resistance will reduce this damage). If you think your enemy will actually attack you while you're both raged and you have blademail, but still want to kill him, if you're sure you're tanky enough, just get mask of madness. It will increase the damage you take by 30%, punishing people even more for attacking you. And if they don't attack you, you only get bonus attack speed, independent lifesteal while you're hitting the enemy, and some movement speed boost if you need it. However, this is obviously risky for tower diving and if there's more than one enemy, as you'll likely quickly die in that case, especially with some sort of lockdown. So this is a high risk - high reward early/early mid game strategy that can either completely screw you, or let you screw everyone, and do it quick.
However, you still have to be careful with this, if you do this to a hero who can actually fight you without spells, and has some sort of lifesteal you're screwed as bs. I've had funny situations of huskar and bs rushing to kill me while playing lifestealer. It's just entertaining to watch people suicide like that thinking they're going to get a kill.
Forcestaff can be a bit of waste on BS, he needs other things more, and it's not that useful unless your enemies are at full hp, etc. It doesn't do all that much damage to forcestaff someone with the ulti up, but it can help you position yourself better and sometimes get away from dangerous situations. So it's very situational I think.
If you are not so sure about tower diving as BS, just get medalion of courage - it gives you a ton of much needed armor, and if you catch an enemy offguard, it will let you kill it that much easily. Also screws people for attacking you back, but only works against physical damage (removing 7 armor from you may be a suicide but provided you also have blademail and outlevel your opponents and they are silenced, this might screw them real bad). It's also just 1200 gold, where blademail is 2200 and MoM is 1800. If you get all three together, that's gradually spent 5200 gold, you can really rape people because they won't be keen on attacking you back, and even if they don't, these items will punish them reeeeeeally bad, since you remove 7 armor with medallion (like desolator), and also have +100 bonus to attack speed from MoM. But you can only do this if you seriously outlevel and outgank your opponents, and if you want to finish the game early (or deny enemies farm by constantly killing all of them) because in any other case, they'll dish more damage and be able to sustain your should-be-painful ganks, so if you're doing badly you should probably build less suicidal items (save for blademail, it should be core on seeker, it actually helps a lot with survivability and mind-fucking games).