Greetings Muley Hunter
Have a good friend who 5 years ago poped the largest Black bear in his county (500+ pounds) in NE Penn with a 270 at 100 yards as he was walking home. Bear folded on the spot. Big black saw him. So yes a 308 with a good bullet will do the same.
But you mention "close encounters" and "charges" ! My up close bear gun (60 yards and less) is a double Fox 12 gauge loaded with .685 round ball cast of wheel weight moving at 1350 fps up to 1550 fps depending on the clothing worn. Two fast shots that you will never feel with a De-excelerator pad mounted. A scope could be mounted but mine has a peep on it with a large white ball up front. This load will far out "thwap" any 308. Yes I also shoot 308's.
But even better would be the Mossy pump 12. Lighter, 5 shots, and with the rifled barrel far more accurate with the same load. 5 fast shots that you will never feel with the De-excelerator pad. And the Mossy makes your fine scope easy mounted. Rig probably weighs hardly more than a bolt rifle and will stop the fight.
So just another route to think about. Browny hunters have used 12 bore with round ball and solid slugs for years in thick stuff.
If I was to use a rifle it would be a 50 something. I am partial to a 50 Alaskan with a flat nose 450 grainer chugging along at 1750 fps. Not a hard conversion on a Marlin 1895. Again a proven rig for big bears up close who have an attitude.
But in the end you will place your life and future into what you carry. When it comes to nasty sharp toothed bity critters I will choose "thwap" over comfort every time.