I've only shot two black bears with handguns, both were one shot kills. The first was killed with a standard 1911 .45 acp with a 220 gr hard cast (wheel weight) bullet. The second was also killed with a hard cast bullet, but a 250 gr one from a 7 ½” Ruger Superblackhawk .44 mag. Both were DIY spot and stalk hunts as Montana does not allow hunting over bait.
Both were shot at under 40 yds with "tight behind the shoulder" hits and both died within 50 yds of where they were shot.
As with most big game animals, I think bullet placement is more important than bullet diameter. My self-imposed limits on handgun hunting ranges for deer or black bears would be about 50 yds for .357 mag or .45 acp, and about 150 yds for .44 mag and larger handguns.
I don’t have scopes on any of my handguns, so I limit my hunting shots to about 75 yds. I am completely satisfied with the performance of my hard cast lead bullets at this range. For longer range hunting, I would probably use jacket bullets which would allow for greater velocity, and I would use a scoped handgun for more accurate shot placement.
Here's the handgun bullets that I've used on black bears.