Send her an email saying you want to ask her something, then you can avoid the lameness of asking for a date by email and lure her in with the mystery of what you will ask her, she will go nuts trying to work it out
Also, if she says no, tell her that's fine and that you will need to get moving to ask your second choice of date. Especially if you mention that it's her friend or some other girl she knows of and competes with, it might be enough to push her into changing her mind.
But only use this if she seems to like you but seems to not want to commit for sure and maybe mentions just wanting to be 'friends'. This means she's not sure if she really likes you yet, but wants to keep you around so no other girl can steal you in case she changes her mind and she thinks you will be one of those lame guys who does that. Girls like that need that push to help them make a decision, plus it shows you are not some clingy, weak, yes man, but someone who can think for themselves and wont put up with their mind game crap, chicks seem to dig that sort of thing.