How do I apologize and approach this girl who I didn't ask out?

[Alex]

Hey guys. I'll tell you exactly what happened. Give some clean and easy info for some advice.
SETTING: First day of high-school (freshman year). - Sitting with a table of 5. A girl name Emily is sitting facing towards the 3 others and me at the table. I sit across this girl name Katie. The other two are guys (typical guys, just saying). [Note] ALL TAKING PLACE IN SOCIAL STUDIES CLASS. The girl whose name is Katie always looked at me and she dated this one guy who name is Carlos but things didn't go well and she posted on Facebook that she isn't interested in dating no more. But, that all change when she noticed me. STORY: Days and weeks later it was in September that I notice her b-day was coming up that following week. Including the dance on Friday. I'm Vietnamese and 14 years old during the time. Katie would always push her desk sometimes against mine. I knew that she liked me but, I was shy and didn't have the BALLS to ask her or talk to her. She liked me and I knew it. After that week desks were changed and were in rows. A U formation of tables was formed in the middle. And desks forming a bigger U around the smaller U formation. I sat on one side of the outer U formation and Katie and Emily on the other side. I had friends with me too. Later after Winter Break, it was February and Valentines was coming up. Katie would always be looking at me from time to time during social studies class. I really wanted to ask her out, but yet again I had no motivation. I was insecure that I would screw things up with my somewhat strict dad. I just imagine being with her. As the school year was about to end I always remembered she kept looking at me all the time. When I caught her, but she looked down at her assignment and continued her task. That last day we were throwing this away such as our projects into the trash and everybody with their backpacks on were by the trash can which was positioned close to the exiting door of our social studies class. I was standing near it throwing my project away when I looked at her expression of maybe I'm over you or I'm upset you didn't ask. I thought it was too late for me.. summer started and I deactivated my Facebook (had around 350 friends, but who cares). So I thought I would just create a Twitter account and relax. I was caught in my past that I wanted to see if she had a Twitter, well she did. But she really didn't post much except from time to time. Probably she had since 7th grade by looking at her first tweet. (She had around 116 tweets currently). Before I explain further more I don't want to be stalker-ish, I just want to give full details on my situation. Anyways, I will paste one of her tweet that give you some of her perspective of what was going on around in Feb. Her Tweet: "Tomorrow is valentines day for some, #foreveralone day for most" - Feb 13th. (Remember during this time I didn't have a Twitter, but I knew that she would feel that way.. Idk my freshman brain hasn't reacted any feelings until now.) So yeah. Sophomore year (typing this on a Saturday after school started 2 days ago.) I feel more confident then I did freshman year now. Anyways during 2nd lunch I saw Katie staring directly at me at a table of friends. I saw her. She wasn't smiling but she sure did notice me. She talked to some friends and walked away or concealing herself from being seen. I don't have any classes with her this semester. Idk about next semester though...

So the 2nd day of school and lunch started like usual mid day. I saw her looking at me again and this time she was with 2 friends. They were heading out to the middle courtyard (center of school) to eat lunch. Her and I had eye contact for 6 seconds. Then, she went out and I saw her sitting down on the cement with her friends. That's it.

I REALLY NEED HELP. I gave a lot of details, but there are some missing pieces in there. Too much to type. I think you guys get the point and where I'm at.

Here is what I thought would be a apology letter. Visit the link: http://www.youtube.com/playlist?list=PLB...ature=plcp (Btw the Twitter profile is fake. Just protecting my identity on that YouTube channel.)

Here are some of what I think would be options for me.
A.) I confront her explaining why I never asked her to be my girlfriend and say sorry.
B.) I direct message her on Twitter the apology letter.
C.) Add an apology letter to the Valentine gift bag this sophomore year.

Any more suggestions? Anything you guys want to say about mine? What should I do? I cry a bit and I'm heart broken right now. Like heart broken alot since I never feel the way I do. Life is short and I know it. I just need some SUGGESTIONS. Please help, please...

I never talked to her, but only a bit. I know she wants me still, yet I don't know if I ever get a chance from her. About KATIE: Her middle name is Rose. She plays soccer and very Katie like. She vis

[Saloni]

sorry TL/DR

[Saloni]

A.) I confront her explaining why I never asked her to be my girlfriend and say sorry.

I think thats the best option.