Nomercy brought up some excellent points. From your OP post and NM's emboldening of it, your primary purpose for the pistol would seem to be a finishing gun. You don't really plan on using it for hunting and "may" use it for grizzlies only if you ever go grizzly hunting one more time.

Based on your statements, it seems like you would be best served by a .22 LR as Nomercy448 stated. However, if you are just torn between a .357 and a .44, get what you think you'll enjoy shooting and use the most. If you ever decide to go grizzly hunting in Alaska again, I know I would take a .44 over a .357 all the time. Let us know what you decide and why.

That would depend on the state a person is hunting in. In some states a .22 rimfire is not a legal firearm to kill big game with, wounded or otherwise.

Very true in that many require a minimum large centerfire handgun to even finish off an animal similar to what would be required to shoot the animal in the first place.

I have to go along with NoMercy448 on this (where legal of course). The only thing that runs through my mind where big bear hunting is involved is why would you consider using a handgun when you should have a rifle of adequate stopping power in the first place. And as far as using a handgun for bear as a defensive weapon in, as you put it, tight quarters I would suggest the largest caliber you can handle. A bear coming down on you will likely only allow you to get one shot off anyway. Maybe two if the first one hits hard enough. The 500 S&W would be my choice.
Just watching bear charges on TV gives me the willies. I had a 300+ lb black bear come at me after I jumped it and gut shot it with the first round. But really don't think he was coming for me, he just didn't know where the first shot came from. The second and third made that point clear to him but too late. (I was using a Rem 760 which is why I was able to get the shots off so fast.)

As a side arm when in bear country I would recommend the 44mag; as it will allow you to practice with lighter ammo, as would the 375.

However, I would want "more" gun in this case !!!

.44mag, Taurus Tracker, 5 shot.

240 or 300gr

I believe what I read prior to purchase for brown bear protection was,
.40+ caliber
200+ grain bullet
1,000+ fps

I wouldn't want a pistol to protect me from a bear, I'd much rather have a rifle and make a killing shot the first time. Or, hunt with a buddy that I can outrun...

Try getting that rifle off your shoulder while walking thru brush with your hands full of fishing gear or hiking with your walking sticks in your hands. The buddy thing is good though.

I know I will hear some crap for this but I did a little research and apparently the bear spray is more effective than trying to dispatch a bear while it is charging at you. From looking at the website and the reviews on it has saved more mauling than using a sidearm.
But I sure as heck would carry a revolver not a semi-auto and here is my reasoning. If you ever and a huge what IF get attacked by a bear and are able to grab your sidearm. Ever pressed a semi auto hard against something and tried firing it? The fact that the slide has to move back the cycle another round is another thing I don't like semi-auto for self defense with a bear. I would choose a light weight 44 mag and if I went the semi auto route if you did not have a 10mm and had a 45 I would buy a .460 Rowland conversion kit for it. If you did not feel like spending all that money or could not borrow a 44 mag.
http://www.fws.gov/mountain-prairie/...ar%20spray.pdf