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.
1. Taming efficiency is going to be quite low during tame and in order to fix that, you need to sacrifice some tames to it
2. Other Bloodstalkers may try to grab you while your already being succ'd, in order to stop that, kill all other Bloodstalkers in the visible area
3. To stop Insect Swarms from interrupting your taming, open your inventory during the taming process, they for some reason don't detect you with your inv open
4. Bring a parachute just in case you are dropped for some reason
5. When he is tamed, only use him to get around and only level Stamina and Health. He is a garbage fighter and if his health gets low, he will start eating you and will kill you but in order to stop yourself from dying, put blood packs in your inv, he will eat those instead until his health is normal again
6. They can be breeded but be warned, when they have an egg, you cannot pick up the egg because it becomes attached to the ground