In most social settings, I'm pretty clear on what's inappropriate and what's appropriate as far as asking for numbers and flirting and stuff, but one place I'm always unsure is the workplace. I'm not talking about me and a co-worker, I'm talking about a girl who works at a store/restaurant you go to.

My example: There's this eatery at my university where you pay like $5 and you basically choose which scoops of random food you want. The service works much like Chipotle. You order, and multiple people do different things down an assembly line. Well one of those girls is really pretty, and she always seems to smile at me (yes, I know it's her job, but it's not always because of that). It's sort of hard to start up conversation since I'd essentially be holding up the line with mindless chit-chat.

What do I do here? I thought about just blatantly asking her if she'd like to hang out some time outside of work, but that just seems so unnatural and perhaps a bit inappropriate. I've been there around closing time and afterwards they all spend a decent amount of time cleaning up and stuff, so that's not really an option either.

TL;DR - Hot girl at assembly-line style eatery, how to ask her out