He would get his ass beat. Bums like the Gracies would have destroyed him at the first UFC, just like they did to all the other martial arts "masters". Bruce Lee's crudentials are shaky as it is, and his meager fighting record (7 fights or so) is even worse. Nobody really knows who won his one big match against the Gung Fu master in SF (most accounts have it recorded as a draw, with the Gung Fu refusing to use kicks for fear of literally killing Bruce Lee).