Hi, I am not a female but I would like to give you an honest advice.
Dude, I see you keep talking about "having that girl, talking to her, asking for her number"... You seem like a nice guy, so why are you trying to get her so hard? It's not like there is not an other girl or something. I mean, she certainly is not the only one. I know you like her, you think she is a great person etc.. that you and her together would be soo happy,"rule the world" and stuff... But, always remember - there is a better one, always. No girl is THE BEST. If you don't start a relationship with her soon, as time goes by you'll find another girl that you'd be attracted to. So why have this pressure now, like she is the only one, if you know that one day she'll be just a memory?
My point is - you should be self-confident, I suppose you have some friends. Go out with them, go to a party, to a meeting, a cafe-bar or some activity that you share with the girls in your college and try to act confidently, try to act a little cocky. Girls like guys that are cocky, self-confident and guys that know what they want.
That gives them a picture of you as a guy that will give them security, and a guy they will be safe and happy with.
So, I'm aware that some people cannot change immediately from shy to cocky, but try it step by step. And yes, that thing with throwing her your number on the table is not acting cocky.
I see acting cocky as the following: acting like you don't need any one of those beautiful girls out there, like not noticing that beauty that everyone falls for. Show them that you are happy with yourself, that you are not desperate for anyone, so I suppose some smart girl will notice that and will start giving you glances etc..
And if you decide, after all, that you would approach a girl, please try doing the following: Do not be too pushy, do not keep on talking and talking... Ask her something simple, like "where are you from", "what classes are you on", "I thought I saw you on that X class last week, was that you?" or something like that. Then LISTEN to what she has to say and give her an answer which will let her know that you were listening to what she had to say, and that you are interested in her, indeed. And all this conversation should not last longer that5-10 minutes, in my opinion. Then, in the end of the conversation, tell her that it was nice talking to her, and that you hope you'll see her some time, have a chat again etc...
That will give her an image of you being confident, but not too pushy. And that should do it.
Then, the rest depends on the situation. Maybe she'll try to contact you, maybe you will. You may just wave your hand when you see her at school, or approach and ask her another simple question. And if there is "chemistry", it will push the things one to another. These things go smoothly.
Hope this helps.
Best wishes