Does anyone know how to start one?

Punch a guy? I needed information from a barkeep for a quest and opted to challenge him to fisticuffs to get the information via talking to him.

I think you can only start them with certain people. I talked to one girl and she said she could kick my butt so I beat her to a pulp......shes now my companion

I dont think you just randomly start it, at least I havent experienced it. I've done three, and one was actually not in a bar but in a mine. They were all quest related though. I was trying to convince someone to do or stop something.