Take the advice from someone a bit older whose been there.
You have to get hit by reality. In real life, love doesn't work like Anime, where if you constantly chase a girl who hates you and show her you love her she'll eventually realize what a good guy you are. She'll think you are obsessed with her, which isn't healthy for the relationship you have with her currently.
You need to ask yourself if she ever knew you liked her. If she did, you MAY have taken too long to ask her, and she sensed a lack of confidence and decided she wasn't for you.
It's unfortunate, but in this world, the girl picks the guy. So you have to make yourself into a guy that a girl would want, and even that doesn't work all the time. I was scared of rejection once too, but now, when I talk to a girl, I gauge her reactions towards me and if they are warm, I continue. If not, then I say "nice to meet you" with handshake, leave, and thank god I figured out that it wasn't right instead of pressure myself with a girl that didn't want me.
You have to wear your confidence, but don't be cocky. Me, personally, I wake up everyday feeling more famous than Drake. That sounds really overconfident, but it's how I get through my day. You don't have to be super athletic. I was lucky, in my freshman year of high school, I was 6'3 and 150 lbs. Talk about skinny, I played basketball. By senior year, I was 6'3, 205 lbs, able to bench 300, and played football. But all throughout high school, I kept my confidence and I did have a good couple of relationships that were a lot of fun (that does really sound a lot like bragging guys, but bear with me).
You learn a lot from girls, trust me. Just go up to her with confidence. If she rejects you, then you can move on to another girl. Don't bank on it, that's life.
If you haven't talked to the girl, go up and have a conversation where you introduce yourself, make yourself heard, talk with her for five minutes or so. Reason I say that is because if you stay longer than that, you may have trouble talking to her more. So tell her that you would love to talk to her again, and it was nice to finally meet her.
Walk away... Talk to her the next day. Even try to make her laugh a little, which is even better if you can do it on the first convo. Talk about something interesting that happened to you or whatever. If you can find something you both like to do (for me, it's normally a girl that likes hooka) then say I'd love to take you sometime and get her number.
Just create an opening or an excuse to talk to her in a way you won't be too nervous. You seem like the nervous type. Let it go. Talk to other girls. EVERYONE gets rejected. I hang around with some of the most charismatic people I've ever met, one looks like a movie star. They all get rejected at one point or another. It's not a big deal, there REALLY are other girls.
Like Beca said, be friends with her. However, too much of friends, and you will be put in the"friend zone". Be sure to be a little flirty.
Zaelous is also right as well, make sure you look nice. Appearances make an impression. If you roll out of bed and don't do anything with your hair, that will reflect you. I personally try to look good whenever I go out, because if I look good, then I feel good. If I feel good, then I'm more confident about myself.