I disagree with you on multiple points. Someone offerings to buy anything, even a Coca Cola, probably has suspect intentions. Alcohol isn't the only thing. Second, the few bucks isn't an issue at all. But a penny saved is a penny earned, right? We are frugal; so sue me. Third, if you think alcohol is what is going to make your girlfriend cheat, then you have bigger problems. People cheat because of who they are as people, not because someone bought them a drink. Yes alcohol impairs judgement, but isn't that taking away your girlfriends agency to say that if someone buys her a drink her intentions are questionable? Do you believe alcohol makes you more likely to cheat?

Again, the alcohol isn't the problem. Someone can be me a fucking bowling ball and it can be assumed they're flirting. As long as no lies are told, no active flirting was done, then what's the harm in accepting a free drink? I was once at a bar waiting to buy a shot for me and a friend and I could not get the bartender's attention. Guy next to me had been waiting longer. We made small talk (I think about the bartender's costume because it was Halloween) and he said, "I'll make you a deal: you get her attention, I'll buy your shots." So am I villainized there because I didn't yell "NO I HAVE A BOYFRIEND?" No. That's not how life works. He takes a risk when he offers to buy a drink before asking questions. Likewise when I've been waiting for drinks I've had guys ask if "I came her alone" and when I point out my boyfriend they move on to another girl. It works both ways.

All of this is completely moot, because that's not what is going on with OP. OP's girlfriend is actively flirting and pretending she doesnt have a boyfriend and making sexual advances at guys so she doesn't have to pay for drinks. Which is also stupid because she could just say "it's my 21st birthday" and half the damn bar would probably buy her a drink.