Why the Bear against the Bull? It probably comes from ancient Roman times when wild animals fought each other to the death in the coliseums for the enjoyment of the crowds. A day of festivities at the Roman Coliseum started with animal fights. Lions fought tigers, wolves battled leopards, and bears battled bulls, etc.
The spectators would often bet money on the outcome of these fights. Typically, a bear would be chained to a bull and they were forced to battle until death. Some days the bull won; other days the bear was victorious. Most often they both died from their wounds.
There is an old Roman saying: Torre et Ursi meritant pecuniment sed Porky non" (The bulls and the bears deserve to make money but the pigs deserve nothing). So the Bull vs. Bear idea has been in the public mind for a long time. Bull and Bear fights were staged in the England of Shakespeare's time and in America in the days of the Wild West.