Some guys are relieved when a girl asks them out because it takes the fear of rejection from them, so don't be afraid to ask him out. Guys have the same insecurities and fear of rejection that girls do, and it's perfectly acceptable for a girl to ask a guy out these days.
As to how long you should wait before asking him out, you just need to play it by ear. If he seems interested, then go ahead and ask him out. Just keep in mind that he may not have the money to pay for a date, so you need to be sure you can either pay for it if he can't (or won't), or plan on doing something that costs very little, or even nothing.
If the guy doesn't want to go out with you, that doesn't necessarily mean he doesn't like you. It could be that he's shy, or that he has other committments. So don't take it personally, and don't let it keep you from asking out other guys you're interested in. Just don't make it a habit of always being the one to ask the guy out because it may make you look desperate.
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There is no set timeline, but it's good to have some rapport and feel comfortable with each other. It's important to gauge his interest and see if there is a mutual connection before asking him out. Trust your instincts and when you feel the time is right, go for it!