Do you two usually chit-chat while you are getting your hair cut?
I don't necessarily mean flirting or anything that would make her uncomfortable, but just basic information gathering and sharing about each other.
The main reason I ask is to get a better idea of why neither of you had anything to say to the other at the bar.
Do you two usually have great conversations and this was a one time freeze up, due to nerves?
More likely, you just need to get to talk more and get to know each other better the next time you're getting your hair cut.
Then your relationship with this woman will move past infatuation to at the very least, a friendship and it will feel more natural to invite her out to do something you share an interest in or to approach each other outside of the hair salon.