For clarification, do you mean “ask a girl out” as in asking someone to accompany you on a lovely date, or do you mean asking someone to “go out” with you, as in go steady?
In my opinion, it always seems like the first one should happen at some point before the second. I remember back in high school people would ask each other to “go out” and next thing you know they’re calling each other boyfriend and girlfriend and they hardly even know each other! I’m not sure of your age, but regardless you should be able to find a way to get in some quality time with someone you’ve been eyeing from afar before going in for the BF/GF status.
That said, I think that a casual “Do you want to grab a drink/coffee/lunch/a snack/a popsicle/a sodie pop with me sometime?” usually works pretty well. It’s not too forward or intrusive, so it would relax her if she’s shy and the thought of a real date makes her anxious. Keep things casual at first unless you think she’s really interested; in which case, I say go for the gusto with the dinner-and-a-movie or something equally date-like. Also, another good way to facilitate a date might be just meeting up with that special someone someplace and offering them a ride home (provided you have some sort of trust), or even just to walk them to their next class. That’s not really a date, but it will get your foot in the door. THEN, after you guys get to know each other a little better, you can maybe ask her to be your special ladyfriend.
Good luck!