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I know I'm comin to the conversation a little late, but here's what I think..
No, don't ask her out right away. If you have never ever talked to her on a personal level before, then you'll need to build the friendship. You don't need to spend a whole lot of time on it, but then again you don't want to walk up to her and say, "You wanna go out!?"
I don't know the best way to explain this. Basically, you don't want to scare her off. There's a good chance of that happening if the first words out of your mouth are asking her out. Like I said above, get to know her a little bit, when you talk to her, talk to her like she's one of your friends and just joke around like you normally would with your friends.
Most importantly, be yourself. If you make yourself out to be someone your not, there's a good chance you'll either get found out, or she'll fall for this fake person and you'll have to come clean down the line.
Hope this helps, and good luck!
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"I was walking down the street with my friend and he said, "I hear music", as if there is any other way you can take it in. You're not special, that's how I receive it too. I tried to taste it but it did not work." - Mitch Hedberg