How do I play against BloodSeeker?

The only real chance you have is using a TP scroll as soon as you notice his ulti is cast on you. And obviously not move any more.

If you move, you will die very quickly.
If you fight, you might not make it.
If you TP immediately, you only have to survive roughly 2 seconds of attacks since he has to walk up to you first before he can start attacking you.

If he carries some way to disable you (Skull Basher or Sheepstick, for example), you're out of luck and have to kill him faster than he can kill you. Lifesteal helps.
If he's not alone, you're probably dead no matter what. At that point, don't get caught alone.

A few options:

• TP as soon as you see him cast / get ruptured. Hopefully he doesn't have a basher.
• IF he does have a basher, ghost scepter + BoT (Or NP's teleport) will get you out fine, as long as you scepter AFTER you get ruptured. Otherwise you'll take 40% more damage.
• If you have an ethereal blade and a TP, you can cast on him and tp out, he'll have a 80% movement slow + be unable to attack for 3 seconds, so you should be fine.
• You can carry a halberd, once you get ruptured, halberd him & TP out, you'll have 4.5 seconds before he can attack again
• Linken's Sphere will also save you if it's not on CD, won't work in high skill games as he'll use silence to dispel first.
• Using a sheepstick or a eul's can save your ass, if you sheep/eul's him + TP you should be able to get out fine.
• Provided he doesn't have a quelling blade or tangos, you can tree yourself in and tele out safely if you're NP. Works for most gankers without aoe / tree cutting abilities.
• If you have an SB, you can just shadowblade and stand still until rupture runs out, then run. If he doesn't have detection and you're not under his tower you'll be fine.

The most important strategy against Bloodseeker: Do not let him get lasthits or denies. This can prove difficult if you don't lane against him or he is jungling, but bloodseeker is fairly weak early on.

Most Bloodseeker builds heavily rely on the HP bonus he gets by killing creeps to stay in lane. Especially with a high range insta-attack hero like sniper you should be able to prevent him from getting lasthits or denies so he can't heal.

This way he will have to get other means of regaining health, costing him either time and experience, or gold. Both will make him weaker if you can continue farming in the meantime.

In regard to your choice of heroes: All of those heroes are viable carriers of Shadowblade. You could try getting that early and then wait for the ulti to end while invisible. But keep in mind: This can only work if you have high enough HP, otherwise Bloodseeker might get truesight on you through his passive.