On a bull? I'd say it depends on skill level like ridgewalker said. Can you get a 6.8 or .243 to work? Sure, but it's not going to bust up a shoulder blade and keep moving on to the vitals.

For the purposes of this thread, I'll say a minimum ethical cartridge for the average skill level would be a .270 with a nice "hard" 150 grain bullet. An '06 with a 180 would be better.