Ok, you're sitting there having a great time with one of the bar girls and you seem to be hitting it off. Next step is to get her from the bar to your room, apt. where ever you are staying. You will ask her, "what is the Bar fine here."? Or, you might say, "How much I pay bar."?
Her reply would be about 200-400 bht for beer bars. Usually it is 300 bht all over Thailand from what I have found. If her English is not good she may not know what you are asking so the mamsan will come over and help you with this. You will then give the money to her or the mamasan and that money goes into the bar register which goes to the bar.
The bar fine is the fee that the bar gets when a girl is taken away from the bar by a customer. She then goes and gets her purse and maybe an overnight bag that have with them and walks out of the bar with you, hand in hand to wherever you want to take her.