Ask her to go out on a Friday or Saturday night. If she says no, then you know she's not into you and you can move on.
If she says yes, just go out and try to enjoy yourself. Just go get drinks somewhere or something casual like that. Don't go with other friends or a group. Be relaxed and have fun, don't try to make it into more than it is. If it doesn't go well, at least you won't have to see each other the next day. If it goes well, see what she says to you on Monday. If she seems stoked, then you probably have the green light for date number two. If it goes really well, then you might be seeing each other in the morning
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I've been out of the game for so long that I don't really have a good judgement of how nerve-racking it can be to ask someone out on a date, but I'm also someone who blew way too many shots back when I was in the game just because I was too poosy to ask girls out. I say take your shot. Not much to lose, but lots to gain.