They used Model 70 Winchester's in 375 HandH.
I just saw this thread. Glad I missed it.
BUT.

On a bet I would cleanly kill a brown bear with my 223 with 53 gr TSX. If I see a grizzly while hunting with my 6.5 Creedmoor and I can sneak up close to it I'll kill it with that.
If I'm going to get in a fight with one I'll use my 458.
Use what you shoot well and fast with. But if your rifle is smaller than a 375 HandH ect. Don't expect the bear to be all magazine article accommodating if you have to stop it at high speed and close range all by yourself miles and miles from anyone and possibly days from medical attention. With no fon service.
But if its a guided hunt its your guides responsibility to insure your safety so just use a reasonable cart with a very good bullet and shoot it well.