I like the .50 Beowulf, but the problem is bullet selection. Basically you are limited to pistol bullets for the S&W class or .50 BMG bullets that won't work in a AR platform
Since bullet construction and sectional density are paramount for charismatic megafauna, I'd swap out the .50 Beowulf upper for the .458 SOCOM if Brown or Polar bears were around - and do everything I could to avoid needing it.
A colleague was in the Coast Guard in Alaska in the late '60s, and they would collect glass floats from Japanese fishing nets that had washed ashore after storms. They'd take the Z boat ashore and take turns covering the activity with an M-16.
Noticing motion in the snow at a distance, binoculars revealed a Polar bear on the move. The .22 on steroids now looked like a pop gun that would do more to annoy the bear than anything, and they made their way back to the cutter and ended their beachcombing.
As a big bear backup, I think I'd stick with the Marlin 1895 with Buffalo Bore 405 jacketed bullets doing 2,000 fps. If you need much more firepower than that, you're in pretty deep kimchee.
BSBD,
Winsor
P.S. This:
https://www.cbsnews.com/news/south-lake-tahoe-bear-california-hank-the-tank-breaks-into-home/
Is pretty much typical of human-bear interaction in the lower 48. I'd much rather relocate it somewhere that it can be a bear without the corruption of a human environment than to kill it for our convenience.