You don't need a 44 mag for bear defense. I'd upgrade the ammo for what you have. I OWN 44 magnums and leave them at home in bear country. You are far more likely to need the gun for 2 legged predators and I choose my outdoors carry guns with that in mind. In the extremely unlikely event of needing to stop a bear standard rounds like 9mm, 40, 45, 10mm, and 357 mag work just fine.
I tend to carry a compact 9mm or 45 if not in bear country. In bear country a G29 in 10mm
No special ammo used in most of these cases and yet they worked 96% of the time.
https://www.ammoland.com/2019/08/ha...r-attack-73-cases-96-effective/#axzz6YEeesaNO
If it makes you sleep better at night invest in some of the better Buffalo Bore or Double Tap ammo. This stuff is expensive, but you aren't going to shoot a bunch of it. Two boxes might last a lifetime.
https://www.wideopenspaces.com/alaska-man-kills-charging-brown-bear-with-a-9mm-pistol/
https://www.buffalobore.com/
https://doubletapammo.com/
For defense purposes shots are going to be close. Precision shots aren't needed and it may take multiple hits. You need something small enough that you will actually carry it and not leave it in the car or pack. Where magnum revolvers come into play is if you're hunting and taking longer shots where precision is important.