I agree with everything that was said, with one exception: there will be occasions that aren't as extreme as a funeral, etc. that she might turn you down for. For example, say she already has a date for Friday night... it would be VERY rude of her to cancel on the date to go out with you, even if she'd PREFER to go out with you. If she's a considerate girl she probably won't drop all her plans just because you asked her out. Besides, you want a woman who keeps her word and doesn't fly into your arms the second you say "hello." A level-headed girl will treat your invitation, and her previous plans, with respect.
But if a girl wants you to ask her out again she will suggest "another time."