I don't see anything wrong with asking out a girl at her work, as long as you know she won't get in trouble and it's not at a busy time.
Go to the grocery store at a slow time, chat her up a bit while she is scanning your groceries and just say something like, "hey you seem like fun, you want to hang out sometime?"
I know it's pretty basic and may seem cheesy but it's quick and you don't have time to lose. It's these types of situations where a direct approach is necessary. It's either make or break time, just go for it. She'll either say yes and offer up her contact information or she'll give you an excuse not to, like she has a boyfriend or something. Don't sweat it if she blows you off, not a big deal, at least you went for it.
Let us know how it goes.
