Politeness as a client or interest? ⇐ Pick Up

[Anonymous]

Got my hair cut at a new barbershop. I liked the way they cut my hair, took the phone number from the hairdresser and started going only to her... I’ve already been several times. During the haircut we chat about this and that, she asks me, she tells me something...the thought flashed through to take the communication to an informal channel, to invite her somewhere. On the other hand, I think maybe this is just formal politeness, and not interest? Although usually before, when I cut my hair, the hairdressers were silent during the process...

It’s clear that it seems like there’s nothing complicated about inviting someone, but on the other hand, I’ve always lived by the rule “don’t give a shit where you live,” i.e. I didn’t have affairs at work, where I buy groceries, where I constantly visit, etc. Plus, if he refuses, going there to get a haircut won’t be a big deal anymore...
In general, what do you think about the advisability of such acquaintances?