You are right, asking her out the first time you see her at her work wouldn't be a good idea. Although, I am pretty sure you can establish a rapport with her in a short time. She works at the grocery store, so you have a pretty good excuse to go shopping there. Start with a harmless converstaion of how her day is going, if she goes to school, etc., go from there and end with a compliment about her smile. She'll remember you next time you shop there. Be confident, relaxed and polite. Dón't forget to smile. Next, try to find a moment when there are no other customers around, and ask her out. I don't see a problem of asking somebody at work, as long as they are not put in a position when there are other people around. It might happen that she sais no (has a boyfriend, or other reasons). Just remain cool and polite, and act natural when you see her next time ( no reason to stop shopping for groceries :-) ).
Another tip coming from a woman - we like compliments. Just do not compliment on any of the body parts when first dating, it's the biggest turn off. Smile is the best to compliment on. Ask questions about her, be interested in who she is. The more she tells you about herself the better you'll know how to act when with her.

Hope this helps,
Good luck.