PM,
I wouldn't think of "when to ask a girl out" and "how many days do I have before she says no?" and instead think of it as, "every day I wait to ask her out decreases the chance she will go out with me." Think of it as a statistical average, and the odds are more and more stacked against you the longer you wait to do so.
Remember, you want to ask her out when the magic is still there (because you just met her, she was excited about you, and she's hoping to see you again) as opposed to a week later when her emotions for you have cooled off (possibly due to her going into auto-rejection that you didn't ask her out quickly after you met her). Ideally, you want to ask her for the date in-person the same moment you meet her while asking for the phone number. If you can arrange the date with her as you get her number, your chances of actually getting the date go way up!
- Franco