How do I go about asking her out?

That's so cute! I think the best way to go about this is to be casual. Ask her if she is doing anything during the weekend and if would like to grab something to eat. OR you can ask her what she likes to eat and be like, "Oh hey me too, I know this awesome ____ place... We should go sometime!" You can do that with movies, places, hobbies, etc. Just make sure you are coy and confident about it. It worked on me a couple times.