Yeah, I don´t know why people have to troll like that. However, after reading the OP, I can see that you have your feet on the ground, and are totally aware of things. I would recommend that you don´t send any money, and see if she want´s to continue the chat relation. My thought are that she will just cut you off. Sounds too much like a scam, that the bar girls are very good at.
However, if she still talk to you everyday and all seems to be good, then you might get a little more involved next time. Not saying you should pay a lot of money, but if you want to keep a bar girl as your girlfriend, it will at least cost you 10k baht per month, and that will be cheap. That´s the point where you have to decide what you think is ok. I can just say, I wouldn´t do it. Far too risky.