I thought the bite alone was sufficient to cause immortality. More like an infection than a transfusion.
So did vampires kill some people by sucking out all their blood, and ‘convert’ others by pumping some in?
If you drink enough of the vampire’s blood you become a vampire (in many of the common mythos, and in my own story). Vampires feed by drinking human blood, but they don’t have to drink enough to kill you.
ETA: I think you may be thinking of werewolves, where being bitten by one and surviving causes you to become one.
If becoming a vampire can heal it, how about a broken neck? That’s obviously lethal or severely crippling damage that even a layman vampire can likely recognize. And it’s the sort of damage a sufficiently brutal man could plausibly inflict with bare hands.
I’ve seen the “get bitten and you become a vampire” idea on occasion as well. Love At First Bite for example; bitten three times, become a vampire.
Yeah, like ex-wives, they need to leave you alive for future feasts.
But if they don’t kill you, do you become a vampire? Or do they have to do something else special to make you a vampire?
Well, as pointed out one classic method dating back at least to Bram Stoker is a blood exchange. The vampire drinks from the mortal, then the mortal drinks from the vampire.