While a carbine or rifle or even a 12 gauge shotgun would be a more dependable option to stop a bear, carrying one while fishing is IMHO impractical. Unless you have a fishing buddy on the bank and you take turns actually holding the gun, it wont do you much good. I havent tried it, but I cant see casting with even a short barreled rifle over my shoulder being comfortable.

A .44 on your hip is a much more feasable option. Its a lot quicker to draw a handgun from a holster then to unsling a rifle your trying to keep out of the way while you fish. And since Id assume more encounters happen when going to or from a fishing spot, carrying a long gun and your flyrod together seems to bring up some other problems compared to the pistol.

The stopping power you lose can be argued either way with too many variables to account for, but I think the convenience of a handgun outweighs those costs. 45ft, or 15 yds is probably the longest shot you should be taking if your trying to claim you were defending yourself from a bear. If it starts charging beyond that, it just gives you more time to steady yourself and prepare to shoot if you need to. That being said, people shoot deer and other medium sized game animals at over 100yds with revolvers so the accuracy depends on the gun and the shooter.

6 rounds from a .44 inside 15 yards should be enough to handle a charging bear. If you cant stop it with that, a carbine or rifle probably wouldnt have been any more helpful.