How to ask a woman out from a bartending standpoint?

I think you should just right out and do it, especially if she's been flirting back with you and has shown signs of interest, and even if her signals are mixed, just strike up a conversation with her and ask her if she has any free time on whatever day to go out and maybe catch a movie and have some dinner or dinner and a few drinks. It doesn't hurt to ask, might hurt to get regrected but it doesn't leave you always wondering what could have happened with that person.