Black bear in the US are not big animals for the most part. Most of them are not much bigger than a hog of the same weight. They appear big because of the hair, but they are thin skinned and not hard to kill.
I hunt with a .45 Colt, but If I were to go to the .44, I would use essentially the same load of a medium hot load with a 260 gr hard cast Kieth SWC. It will shoot into the vitals of, and through most bears.
I would never, ever shoot at an elk at 250 yards with a handgun. At 50 yards, I would feel confident that my loads of 10 gr of Unique under that 260 would anchor that elk. At 50 yards this load will enter and exit lengthwise, a good big Muley buck. I have killed a lot of deer with this load, and have yet to recover a bullet.
I spent many years logging in New Mexico and have been around a lot of bears. At the first whiff of a human, most bears will be heading out the other way just as fast as they can go. I only shot one bear in all those years~~I woke up one night to find one had stuck his head inside the flap of my tent and was looking around. I eased my .45 up to his head and dropped him right there, a record setting 1-1/2" shot. Unless you get between a sow and her cubs, you will not see a bear stand its ground.
Grizzly is a different critter. I would not go into griz country with less than a 12 ga with slugs.