Short for "bar girl". A girl who works in a bar or strip club whose job it is to get guys to buy the the most expensive drinks in the bar, like champagne, and run up large tabs by flirting with the customers and implying she is sexually interested in said drunken sap.
Sometimes the expression is used to refer to prostitutes associated with particular bars and who run this scam as well as hooking.
Foolish drunk man: "I asked this hot chick if she wanted a drink and she ordered a bottle of Dom on my credit card!"
Friend of FDM: "Dude, she's a b-girl moron! Let's quietly leave before it gets here."