Most vampires aren't stupid enough to attack a group unless they have a reason so you might want to add something. Perhaps Emma was dared into going into a condemned building the vampire was using as a hideout. Or she disturbed a nest. Vampires would be the more common of the supernatural phenomena so the D.I.S isn't going to be dispatching teams unless they are causing noticeable problems like consistent killings.

In this mythos Vampires disintegrate when stabbed with a stake so Emma should mention something about that.

While I like the character and she'd clash very well with mine I think we need a little more information about her background. Exactly how did she end up getting a job at the D.I.S, why did they choose her, was this right after the attack or several years later, did she move to LA before or after getting the job, what is her family like does she have any extended family or siblings.

Was she apprehensive or eager to join the D.I.S, you said she was apprehensive and not ten words later she joined as soon as she could, which is it?

I like the character itself but there are too many unknowns about her past.