If I went back to Alaska where the bear get huge, I would indeed go with a 45-70 as minimum bear gun for just being in the woods. For hunting, I believe the .375 H&H magnum is the real minimum and many go higher than that. Bullet placement is key, but I believe to stop a charging bear, you really need a lot behind that bullet placement.
I consider my .444 as a minimum woods gun that could do the job, but it is not the most optimal for the job. It is at or a little above the 30-06 in actually power. Smaller guns have taken bear, even revolvers such as the .44 magnum which I now have for a woods gun in Idaho NEAR town. When out further, it will be the .444 AND my .44 as back up with plenty of ammo since they have increasing numbers of wolves in the area up there. I also have a 300 WSM that I wouldn't hesitate to use in an emergency situation, but I would feel better using something more than a 180 gr bullet no matter how fast it is going. That brings us back to the .338 and up.
One of my friends tells the story of his father having to cancel a trip to Alaska in the 1960's I believe but his friends went anyway. They never returned. They found their dead bodies beside a giant brown bear that died also as a result of all of their shots, but he got them first before dying. They are big, and fast and when they want to be can kill with a single swipe of their paws.