I'm an extremely lightweight drinker and didn't hang out much in bars, so I find this really fascinating. If I'm out with friends, of course we would take turns with rounds, but it would never occur to me to buy a drink back for some random person I'd just met, even if they bought me one first. (Nobody's ever bought me a drink full stop so I'll admit I just totally don't get any of the "etiquette.") I tip bartenders and service staff very well, so I also wouldn't think of buying them a drink. I can't imagine most women would have any idea that that sort of reciprocation is expected or would be welcomed.

You learn something new every day!