stop hesitating, there's that old saw:
He who hesitates is lost.
Remember, it doesn't matter how scared you are, so is she.
Smile, say good morning, ask her if she fancies a coffee, just do something. The world won't open up and swallow you, no thunder and lightning to strike you down.
The chances are, she'll say no, they always do, they like to have time to think: 'mmm, the next time he asks me I'll say yes.'
Boys are more grateful that someone likes them enough to talk to them and they say yes straight away, well, after they've stopped spluttering and managed to regain control of the tongue:-)