With regard to the police, I'd tell them exactly what I saw and transpired. As for myself, it's not likely I would assume I was almost bitten by a 'real vampire'; chances are, if anything, I'd tell the cops my attacker was dressed up as, or acting like a vampire.
Basically, without some hard evidence, I would interpret what happened as an attack by a weirdo (I mean, why would a real vampire run from the police; they couldn't stop him, and he could take them out as well).
If hard evidence of a real vampire was available...well, that would 'inspire' something of a reboot of how I see the universe. Whenever I watch vampire / demon movies, I'm always figuring, 'Well, if supernatural evil exists, then supernatural good must exist'.
I might also Thank God that at least it wasn't an anal-probing alien.