I just read an interesting article on rifles and guns used for bear hunting and for back up weapons on bear hunts. I find it interesting how paranoid certain people are about black bears, even though they can be dangerous the likelyhood of being attacked is quite scant. This does not mean you should view bear hunting light hearted as you definately need adequate firepower to respectfully and ethically harvest a bear, lets look at some options for bear fire power;
Rifles– Bolt action is the most reliable action so it only make sense that this should be your optimal choice for a bear hunting weapon. I would say that a .30 caliber rifle is a good choice such as a .30/06 .300wm, .300 ultra mag, .300wsm, .300 weatherby, .338 wm these rifles will definately serve as great bear hunting guns. If targeting grizzly, brown bear, or polar bears, you might want to start with a .338 wm and move up towards a .458 wm. Even though many a grizzly have been taken with a good ole .3006, you might want to lean on the heavier side of armament when tackling the great northern beasts. For bullet weight I would look at 180grains and up with properties that have slow expansion and wieght retention.
Shotguns– I definately would not opt for a shotgun to hunt bears but if you are in a zone that prohibits rifles you could use a shotgun with a saboted slug load or some heavy buckshot in your 12 gauge. Pump action is probably your most reliable action to use, and a defender short barreled shotgun is a popular choice for bowhunters wanting the comfort of a plan B.
Bows and Arrows– Kinetic Energy is an important consideration when using archery tackle to kill bears but a sharp deadly broadhead is key to the whole operation. For Black bears you should be at 50ft.lbs. of K.E. while the K.E. required for grizzly bear is 65ft.lbs. Broadheads should be 100grains+ depending on your arrow wieght which plays into your total kinetic energy.
I hope this information helps as spring bear hunting season is now on where I hunt!