I moved on, but I always come back to her?

It's no ordinary story but I am in need for some advice on what I can do, or say. Any thoughts appreciated and thanks for you're time. :)

junior in high school I'm mainly asking for some analysis and some advice on what I can do. First of all In the begging of the school year I sat next to a girl simply because she was cute and caught my eye she's 16 too..anyway as I sat next to her she tried to pass a paper to someone else but it was across from where I was sitting so I did the generous thing and I grabbed the paper and handed it across. I thought she would say something or at least give me a thanks. I tried to give eye contact too but didn't give it she just looked somewhere else but she knew what I trying to do...So I told her " You know its nice to say thanks when someone does something nice for you" I said it playfully and shot a smile, and she just said "thanks" that was it..So next day comes and she sits somewhere else, I didn't care to much but what could it mean? As time went on she tired to stand next next me and she would be fixing herself like hair,etc... Another time she walked right up to me like if she wanted to say something, she stood in front of me (almost like at an angle) So I decided to say something I told her"hi" and she looked at the floor instantly then looked straight ahead but never game me any contact and she was tense, I'm guessing she was nervous because she said a small "hi" back I just left the area... Next time, in lunch I caught her staring at me., We stared at each other for a good couple seconds. Another time I was standing talking to my bud and she walks by me and bumps my elbow on purpose I know she did because there was a lot of space from where she was walking what could that mean? Anyway I never got a chance to meet her now I realized how much of an Idiot I was and I learned a lesson. As I never got to meet her school ended. I tried friend request and message her on Facebook I'm too old school for it so I don't know if It was a good Idea. I just said how I didn't get a chance to meet her etc..(she also changed stats form a relationship to single) and she ignored me I sent another one a week later this time I just said how I thought we were gonna be pals, but I said it playfully, I know she ignored me because she updated her stats as time went on. I didn't mean to crawl on her but I saw a picture with her and some guy I guess it was her ex boyfriend, and she seemed fun and confident with that guy, and others too because I took notice within class. But at that time she was nervous with me what could that mean? So anyway school is gonna start up again what am I going to do when I see her? I don't want to go up to her and say "Why have you been ignoring me"?

I'm really frozen up on what to do once I see her. Please excuse the elongated paragraph but I'm just trying to get an answer here, I don't its a done deal in entirety but what can I do.

I'd say back off a bit. I think you've creeped her out a bit by acting too keen, and its making her recoil. Just be cool, try not to initiate conversation unless absolutely necessary. Unfortunately you're a bit stuck in this situation, as initiating conversation will push her away more. If you get the chance to speak to her without forcing the issue yourself, don't stare at her or any of that, just smile and be pleasant. Sometimes "staring" can be misconstrued. I stare at people all the time, it doesn't mean anything.