Should i ask out a female co-worker?

Okay, for starters my situation doesn't exactly match the generic scenarios I've come across on the plethora of websites dedicated to this question.

I see this girl occasionally at my work and have had the awesome pleasure of working with her a couple times. When we made small talk, we found some common ground (we both go to college and plan to move east). While attractive, intelligent and sweet, she is introverted and it doesn't sound like she goes out much. I know I've caught her looking at me and flashing smiles, but I'm not sure if that is something special for me or something she "just does".

The details:

I work security and see this girl maybe once a week while on patrol, but I foresee this assignment ending for me so I might never see her again (a curse because I have limited time to pounce, but maybe a blessing if this blows up in my face because I won't have to see her everyday?). I think she knows I've been kinda going out of my way to make these visits.

While I'm not really her supervisor, I do "outrank" her and am on track for a supervisory position, though not exactly one involving supervising her. Its a ten dollar an hour job, so it's not exactly like it's a "dating professionals" environment involving terms like "career choice" and "water cooler gossip".

I already like this girl, enough so that I haven't exactly been on my "A-game" while making my little visits to see her. Hopefully I am not already condemned to the uncomfortable pit where creepy and lame join.

The plan thus far: we both take classes. She's good at math, I'm not. I'm thinking "yeah, I just registered for classes, but this math class is gonna be rough. Say, do you think you could help me out if I get stuck on some of the material. Really? Wow, thanks! Here, let me get your number." Weekend comes, I ask ftext for help "its kind of long to text, maybe I could show you over coffee. My treat for the help".

Whad'ya think? Thanks guys and (hopefully) girls.