I think asking a girl "Do you like me?" is pretty lame, to be honest. It puts her in a really difficult position. If she’s polite, she might not want to hurt your feelings and just say yes when she doesn’t really mean it. Or maybe she likes you just as a friend.
And even if she does like you, she may well say ‘no’ because she thinks it is some kind of trick question or she fears rejection or is shy. So even if you did ask her, you wouldn’t know if her answer is sincere or not.
Much better, I believe, to just ask her if she’d like to have lunch together or hang out sometime. If she’s interested, she’ll probably say yes.
Or if you’re brave enough, to be honest, and want her to know how you feel, you could tell her you like her and see what she says. Hopefully, she’ll say ‘I like you, too.’
It seems unfair to expect her to be the first to say how she feels. If you like her, tell her. She might not have considered you as a potential boyfriend before, but she’ll at least give it some thought if she knows you like her enough to approach her.