Would a vampire biting someone's neck be safe? Like possible diseases aside, where would be relatively safe places to bite without possibly causing the person to bleed out?
So the problem with vamp mythology is that vampire bites tend to go for the artery (the neck, for example), which tend to bleed…. well, a lot. The wrist is another common target.
But really, nicking an artery anywhere is perfectly liable to be lethal.
I’ve seen this countered in vampire mythos in setups where the vamp’s spittle is a coagulant, and so they drink and then lick the wound to seal the blood vessel. I think this is a fine idea, and a perfectly reasonable adaptation: if a vamp can keep a victim (or thrall) alive, they can drink from the same well repeatedly, though realize that it takes about 42 days for a human to regenerate the blood lost from a donation, so if they are drinking solely from thralls, they’ll need quite a large group (depending on the volume the vamp needs to consume to stay alive).
Other locations vamps could bite but typically don’t: The inside of the thigh (femoral artery), the foot (pedalis dorsis), the back of the knee (popliteal artery), the elbow (brachial artery), the wrist (radial or ulnar artery), the inside of the ankle (medial malleolus). A good bite on the clavicle could even get at the subclavian artery, but the vamp would have to come from over the shoulder unless they have bottom fangs as well as topfangs.
If you have a willing partner, I would suggest you try to put your teeth around places where vampires supposedly bite and work out the logistics of things. Human teeth are designed more to rip than they are to actually puncture, meaning that if you or I bit someone the way vampires are supposed to, we would rip the skin off before we punctured the artery.
Biting things is surprisingly awkward.
Also realize that humans require pressure from both halves of the bite pattern in order to actually get the leverage to puncture anything. We don’t just produce a single clean hole, but a whole ring of tooth marks. Even with elongated canines* (fangs), we still need a way to apply that force, which still implies applying force with the jaw.
I hope this was helpful! Good luck with your mythbuilding!