Why would a vampire begin a relationship with a human being? It's a recipe for a disaster. The existence of the parasitic race of blood suckers is and must remain secret. Revealing your existence to one of the herd carries with it a sentence of death, for the transgressor and the human who learns of their existence.
So why would a vampire violate that commandment? The most obvious reason is to feel like a person. Vampires find the pleasure of sex minor in comparison to feeding on blood, but that doesn't prevent them from liking and wanting it all the same. The ritual aspects of human seduction are sometimes visceral pleasures in and of themselves to the undead: being able to walk into a room and walk out with any man or woman you want is a powerful ego boost for a living deadwoman... even if all she does is walk the fellow home, take a quick bite on the neck, and slip away.
The rituals of relationships, too, can form a basis for reconnecting with a diminished moral compass. A Friday night date at the park, just after sunset, with kisses on bridges and glass of wine discretely poured into the bushes when her partner isn't looking, can do wonders to soothe the soulless.
My character is a vampire. Not an old one or a powerful one, but one that has been a monster just long enough to be able to kill when she has to, but not long enough to not feel bad about it afterwards. One night, out on her own, she meets your character, who approaches her with romantic or seductive intent. Acting against her better judgment, my character accepts your character's advances, goes on a date, and...everything afterwards. Somewhere along the line, your character discovers the truth.
Now my character is in a bind. Letting your character go with the knowledge of what she is is impossible. But she doesn't want to kill you either. Not after you've been so sweet to her. Not after being with you has been the closest she's felt to being alive in so many years.
So we end up with a twisted Scheherazade thing happening. Your character's life hinges on his or her ability to keep the fire of romance burning with the monster holding her prisoner. Mine is working up the courage to kill yours, but paradoxically puts herself in a position where she's being courted and wooed and falling more and more deeply in love with yours.
Once this tension plays out, we can decide how it ends.