a lot of professors are professors for that reason.
It's inappropriate, but still happens. I'd see girls and my professor out keeping it lowkey, but if you watched long enough you'd see the 'feels' and rubs...then the two leaving at the same time about 20 seconds apart.
The stuff happens, it happens in business too....sex is the #1 commodity, I have had my employees offer it for favors which I didn't do and I have had classmates offer it for help which I sometimes did (I may have been guilty of suggesting it though

).
I say do what you want, you are the one in the boat. There is nothing wrong with talking to her and seeing where it goes. If she is playing you or not. If she is really interested, suggest after the term hooking up (as long as the college allows it...some don't care as long as they are not your students or have potential to be one, some prohibit any teacher/student relationships).