Originally Posted by JonM
police and game wardens in alaska pretty much all use 12ga 3inch magnum slugs in a pump gun. prolly a good reason they all use those over handguns.
I don't normally comment on these bear defense questions, because I have no experience in the matter. But, I do follow the comments most times. The "bear" minimum is generally regarded to be the .44 mag in a handgun, but bigger if you can get it, such as the .500 or .460 that you already said is out of reach for you.
But, the biggest consensus is what JonM just mentioned. 12 gauge with slugs, or a LARGE bore rifle, such as the .45-70.
It seems to me, just by browsing the internet, if you look at a gun manufacturer's website and they have an "Alaskan" model, or "big game", or "Safari" model of a rifle, you may want to look at those chamberings to get some ideas on the "bear" minimum you may need.
(Y'all see what I did there? I'm a dork.)