Sure, a Mosin Nagant is a most excellent Bear rifle.
I hunt Brown bears, Black bears and my son does too, as well as a couple Polar bears now.
Of the 17 or so Browns Ive caught in the Spring hunt, 11 were with a Mosin.
The first vid is a double head shot with open sights at 400or so yards,Sako M-39 variation with Czeck FMJ's milsurp, Bear was an inch shy of 8 feet all my shots passed through.
My wife used her Valmet made M-39 with Czeck ammo as well and this is her first Brown Bear, squared 10'2". This guy musta been in a salmon hotspot all fall, it had nearly 5 inches of fat!!!!!!
First shot was about 250 yards, the second maby 300 as he ran off Both of her shots were pass throughs.2 hits to the neck ripped out its throat arteries and he ran 75/100 yards before collapsing and dying.
Were in wide open country and longer shots are often, but were used to it.
If you Mosin is accurate, your ammo consistant and you can shoot straight, a Mosin will do everything needed to make all kindsa big animals dead, Moose, Bears, Wolves, Caribou, Muskoxen, Walrus.