If it is a real thing, and she makes a real move, react to it then. If it isn't really happening and you make a move, you risk losing a lot of future help cause that is a fast way to getting dropped as a friend in this situation. If you are actually a friendly person and talk to professors, a lot will be friendly back because so many people don't give a single shit other than getting the letter grade and moving on. I maintained friendships with 3 of my professors during my undergrad time and they made it very clear that students rarely, if ever, see them as more than an outlet for a letter grade. So you are likely getting the attention because you see the professor as more than just an object to give you a grade.
Best advise, let her make the first move if she is really interested. She has the most power in the situation so it is really up to her to initiate this if it is real just imo. Otherwise just be an adult and be friends.
As Celista said, I also don't think she is really into you, just you are a friend so you stand out in the crowd of faces that don't give a shit about being her friend.