that sounds great and please do write it and hand it in
however, for the contest, they only take entries up to 3000 words - though you can expand the story afterward. So perhaps write a snippet from your storyline that you find most interesting for the reader
How to meet, some ideas:
A silly hobby after-class or even something considered more sophisticated? Chess? Or even maybe a very old game - Go? (vampire could be pretty old and of Asian descent)
Visiting an old friend in the hospital who’s dying? Could be a former LI of the vampire, and relative to the new LI?
hmm, only thing that came out right of the top of my mind but maybe it helps form another new idea