I highly recommend trapping them inside a structure to close yourself off from the swarm, once you dismount a creature you'll get targeted and that can screw up your taming. I used 4 dino gateways with 2 dino gates to close both the bloodstalker and myself off from the swarm. Then just let it eat the blood packs from your inventory until tamed.

More Bloodstalker Taming & KO Tips