There is nothing inherently beta about the act of buying someone a drink. Alphas buy people drinks all the time (actually moreso than betas, if my empirical observations serve me correctly). It all depends on why you're doing it.
I've had alpha guys buy me drinks before, usually because I told them a cool story or something and they wanted me to stick around and talk to them more. Which is totally normal, because alphas in bars have all the time in the world. They talk to everyone and have a great time doing it. Hell, I've had girls do it too... but those were usually my bartenders, and they were doing it to get my goodwill and ensure that the tips keep rolling in.
If you're doing it to build attraction or rapport, it's a bad idea.
If you're doing it to
demonstrate to her that it's okay for her to have rapport
with you, then it's fine.
Subtle difference, but important.
As a general rule, buy the girl a drink, IF YOU WANT, if she does something really awesome. Tells you a cool joke, funny story, whatever. If the girl is seeking rapport with you and qualifying herself to you, go ahead and buy the drink to demonstrate that you think she's cool.
A girl asking for a drink, however, is just asking for trouble. Make her jump through a hoop if she does that. Preferably a makeout-sized hoop. The idea here is to make sure you aren't getting played. A girl may ask you for a drink as a token of comfort, in which case it's cool to buy her one. But if she's just hustling you, make out with her first as a down payment of sorts.
And if she takes off after that, oh well. You just made out with a hot chick for the price of one drink. There are worse things to spend your money on.
