Next time you see her in your normal course of doing things, pull her aside and ask her if she has a quick minute--most likely she will...then come out with it. Worst comes to worst if the time is really NEVER there, you can always say hi and hand her a pre-written note. Don't worry it's not cheesey...i had the same situation a while back and the girl thought the note was very cute since we never really had time to talk...and yes it worked out well
On a side note.....I know the feeling you probably have right now...don't think this out too much. it's really not as big a deal as you think. There's PLENTY of girls out there, and you sound like a decent guy--you should have no trouble finding someone if you keep cool, natural, and real. good luck man--let us know how it turns out!