Should I Dance with Her?

I am a Sophomore at a private high school. Each grade has about 100 kids in it, so everyone gets to know everyone, especially people in our own grade. There's this girl. She's in one of my classes, and she's in my grade. She was the first new person that I talked to at this school, which was about 5 months before our Freshman year started with the placement test. She's really pretty and extremely nice. She didn't have a lot of friends in middle school, but now she has tons and she hangs out with a lot of boys, half of which are guys I wouldn't expect her to talk to. I'm not making a bad name of her or those guys (I try not to, but I could be one of them), but I find it rather odd that she talks to them. I've felt kind of a connection between her and I. But she's kind of that way with everyone, and, sometimes, I don't even talk to her as much as other guys because I get nervous about approaching her. I stutter, forget what I want to say, and make a near fool of myself when I'm around her since I've started liking her. On our first day of school, I saw her, she gave me a hug, and she told me about her vacation. In the middle of the day, I told her I liked her. She was happy that I told her, but she said she has a relationship with a guy she met in Portugal. Feeling disappointed in myself and her and a lot of other things, I asked her if she would go to the Homecoming dance with me. She said she would think about it. I think she felt bad about it, because she wanted me to sit next to her and her friends at an assembly soon after. She said this wouldn't change our friendship, but at the same time, it kills me to know that she doesn't like me like I do. From then to now, we have been discussing our feelings, because I don't think she likes me as much as other guys. She told me she doesn't feel that way and that she actually tries to be my friend more than she tries to be friends with other guys and I take things too seriously. She's right, because I get really jealous of her and then try to stop talking to her for good, but we both know that I can't leave her. Tonight is the dance, and I'm still at this standstill with her of me trying to stop liking her and her trying to be her own person. So should I ask her to dance tonight? What are the things that I'm doing wrong? Can I get her to like me? Other things? Thanks