If this happened to me, I just wouldn't be able to take the guy seriously (after this happening to me several times) I'd assume he just wants to take me out simply because he's physically attracted to me and he'll probably end up ditching me. They are usually really nice guys who will take me out on 2-3 dates. After the 2nd or 3rd date, they suddenly ignore me, ditch me, and find another pretty girl to date. Doesn't matter if I slept with them or not. They ditch me regardless. Hope you don't turn out that way!
Take a chance, what's the worst she'll say? No? There's plenty of others out there who I'm sure would love to go out and you can't give up on one try. I say be yourself and keep it cool, ask in a respectful and confident way. Sound like you mean it and don't hesitate. Wish you the best of luck!