So I'd love to have a twist on vampires, but I don't want to stray too far away from the theme. Essentially if it's a character that bites and drinks blood, does that alone qualify?

hmm i'd say as long as it's still recognizable as a vampire (which i think still having to drink blood is recognizable enough) i'd say you're good. there are soooo many different interpretations of vampires, it's fine for people to add their own twists to them - we don't expect everyone to just be writing dracula-types!