Asking out anyone in the service industry is hard since they are playing up to you to begin with (if they are good at customer service).
I am a talker, so it makes it even harder....I have found asking some open-ended questions during the 'cuts' can let you know if she is interested. It's a delicate thing though and I don't know how to explain it, but if she is interested she will 'close' the questions sort of. Maybe something like "It's so hard to meet a cool lady lately, where are places someone like you hangs out?" I don't know if I'd use that but that's a perfect example....throw in a compliment and a question, see if she bites....if she is interested and knows you are looking, she will hint at herself more than likely.
I would ask her to a lunch regardless, it's an easier ordeal for a woman (or man), you know you have to be back at work so there is no wonder what happens after we eat.....
That said I don't know if I'd date a hair dresser from my experience....they seem either the marriage minded/commitment type or total party girls nothing in between like dating and gettng to know each other first for a long time for an eventual commitment...not trying to stereotype all of them, but in my experience that is what I found.