Your going to get a zillion opinions, none of them are wrong, most are partly right!
To stick with your original questions, take a look at Rottweil (?) slug loads maybe found under the name Brenneke also. They are slightly smaller in dia. than other slugs made for smoothbores, and a LOT harder lead alloy. The slug (rifled) also sports a more pointed tip.
A freind told me of an instance when multiple slug rounds were "shrugged -off" by a brown bear in their camp. He was in a canoe approaching the camp and the critter was mauling their poorly stored ice-chest to get to the 2 liter Coke bottles! He stated that they hit it 2 or 3 times with traditional 12ga. slugs broadside - don't recall the distance, but he said the hits were visually obvious and the bear wasn't giving up his Coke until multiple shots hit him near the shoulder area.
I am very reluctant to believe that story 100%, the adrenaline and age of the teller were at opposite ends of the scale. If there is any thing to be taken from it, the message is that common slugs don't have great penetration power. I have seen 3" mag slugs mushroom and stop with NO PENETRATION against the door of a 70's Chrysler New Yorker from about 25 feet. Bears aren't cars, but, if I'm going to shoot at one (not to protect an ice chest!) the goal is to kill it before it kills me or one of my party.
Second hand quote from a Coast Guard guy stationed on Kodiak Island for search and rescue: "A lot of the dead hunters we find from bear attacks had a pistol in their hands or nearby".
A revolver is good to have, but if an attacking animal is too close for a short-barreled shotgun, it will likely do some serious damage to you even after being hit. Big bears are tough to kill, and are noted for continuing a battle even when mortally wounded, then after putting down their adversary (you) they limp away and die.
AK Fish and Game Dept. has some good info. on shot placement /advice for bear hunters. The recurring message in their info. is make sure your shot placement "breaks down" the bear. This means shoulder or spine shots to anchor it where it's at -nobody likes a wounded bear. Their bones are huge and tough. Furthermore, their skulls are thick and brain not too big!
The first bear I bagged was a 6' black, pulled the first shot and hit the spine between ribs and hip. It fell/squatted only long enough for a quick follow up shot on the front shoulder, hitting the heart and breaking the far side bone in two. First hit paralyzed, but only the back half, not the front half with the dangerous parts! The first slug was totally absorbed into the spine, no exit, no breakage of bone!!! That was a 175gr. from factory loaded 7mm Rem. mag. at ~ 150 meters.
That is just my own experience illustrating the toughness of the smallest of the 3 bears you may encounter in northern country.
The effective range of a smoothbore 12 ga. isn't great. Again opinions are heavy on this, but I would guess ~50 meters or less for accuracy and not much more than 75 for good stopping power on a big bear. It could benefit you greatly to try some different types of ammo to see what gives best accuracy, be ready for a sore shoulder!