DUde!!!
Get you check ride done first, then take her out to dinner as a way to say thankyou for her time, and see how it goes from there. You will have a good Idea by this point as what to do next.
p.s. I just had one of the female emt's hit on me and she knows my wife very well. Try dealing with this and working 24hrs and staying in the same apartment (one of our stations) just the 2 of us!!! And she's very hot, red head, and 6 years older than me. She is also engaged, and has twin daughters. Man I can't wait to get to Montana...