I recently started getting some help on my English papers, with a tutor from my university. This tutor is a recent grad from a local university, and happens to be my age.
She is a really good looking girl (8.5 on Miami scale), a bit shy and reserved, and quite smart.
When she helped me out, I always kept it about school. We were never alone, she always was helping multiple students and could have (maybe) got in trouble for giving out a phone number.
But one thing I did was make her smile and laugh, and at times we went off into irrelevant conversation ending with eye contact and a smile. I felt like I should have gone for a number close the last day I saw her, and didn't.

My question is:

I know her name, and can try contacting her through Facebook?
Is that creepy?
If no, how should I go about initiating?

I know Facebook is convenient, but that was the last time I will see her due to her finding a new job.

What are my options?

Facebook could be creepy depending on how you go about it. If I was to use facebook I would find her and then say. Hey I'm having some problems with these questions(school work or whatever you getting tutored on) And you seem like the only one I can really understand. What do you think about maybe having a private session with me to help me. Since she likes doing stuff like this, she will most likely bite the bait. Then when she get over there have some mock up questions that she can solve for you and then once you get that over with. Just be yourself and ask her what her goals are and get more personal. It won't be hard if you have her already at your location. But if you see her on a regular basis around the campus or something. It's best to just go in direct and ask her if she will be willing to help you out privately somewhere, and skip facebook altogether.