I watched a video of a brown bear shot at close range with a .338 magnum. The bear bluff charged first and the hunter waited until the bear turned to leave. The first shot was in the boiler room, and rolled the bear. He got up and kept moving. Repeated until the last shot in the rifle. The last shot fortunately hit the shoulder and stopped the bear, but didn't kill it. The hunter was using a borrowed Browning, and the magazine has to be attached to the floorplate before closing. He wasn't familiar with it and it took him quite a while to figure it out. His hands may have been shaking. IIRC the gun held 4 rounds. If that last shot hadn't crippled the bear, he could have charged and killed the hunter. If he had fired at the bear while it was bluff charging, he probably would have been mauled. Until I saw that video, I had no idea how hard it can be to kill a brown bear.
I used a .30-06 to kill a black bear at 15 ft. once. Hit it in the throat and it only went a few yards. At 15 ft. all you see through the scope is hair. I got see-through scope rings after that.
Maybe use .280's and bear spray.