Will a vampire bite on the wrist cause the victim to turn?

In Abrahim Lincoln: Vampire Hunter movie(lol), biting the wrist kinda like poison the victim and lead to slow death

I think it depends on the victims personality. Some might turn and run. Others may start to punch the sucker to death.

Is it set in a set universe (Superntural, Buffy, Hellsing, Vampire: The Masquerade, etc)? If not you decide how it works.

Depends on your personal lore for your story. It is YOUR story, you decide. I've seen a lot of various vampire movies/shows, read a few vampire novels.. It really is a mixed bag of what turns a human into one.

Ghoul. He will become a ghoul.

Why don't you like, create your own story with, like, your own rules and stuff.

Depends on the "universe Lore", it may cause the Victim to: die, to become a ghoul(also requires the vampire feeding his blood to the victim), to become a vampire or simply nothing happens at all.

Your story, your rules but if it's some inspiration you seek why not have the person afflicted by the vampire "wrist nibble" to have hallucinations and a predetermined amount of time to kill the vampire before they sink into madness or whatever calamity you have in mind? Makes for a decent plot imo.

Lol you are writing the story you can do whatever.

Just look for sparkles in daylight. If you've got sparkles watch the ending of Terminator for a worthy suicide idea.