What dialogue/scene reveals that Bert had previously broken Fats?
I don't recall anything.

Bert was using Eddie to hustle Findley. He knew that once Eddie had made the choice to stay and play rather than go with the woman he loved (and who loved him) that he had broken him and owned him. Bert realized that Eddie was willing to give up everything else in his life that mattered in order to win and Bert knew that was the moment to raise the stakes with Findley. Bert was the true villian of the movie, and knew how to break people. He broke Minnesota Fats (before we see him on screen), he broke Eddie, he broke Findley and he broke Sarah.