I have ruled out shot guns based on research, here is a little snippet from chuck hawks on the detractors of using a shot gun;
Of course, while powerful rifles are the best defense against bears, other choices are possible. The possible alternatives are shotguns shooting "rifled slug" loads or powerful handguns, usually in the form of magnum revolvers.
Let's consider shotguns first. Frankly, I can see no point to buying any sort of shotgun for dedicated bear defense. A shotgun is just as heavy as a rifle, just as long and costs just as much, so it has no advantage in either size or weight. A shotgun shooting slugs is markedly less accurate than a rifle and bullet placement is the single most important factor in stopping power. It is no easier to carry a short-barreled shotgun in the field than a short-barreled rifle, so you might as well tote the superior rifle.
Despite the claims of those selling special shotgun (i.e. slug type) ammunition or special barrels to shoot slugs, the reality is that almost any heavy for caliber, high powered rifle bullet, particularly the premium bullets typically used for stopping big bears, has far more penetration than a 12 gauge shotgun slug. Such rifle bullets will reach the vitals of a brown bear from practically any angle, which a shotgun slug is unlikely to do.
The reason is that, while shotgun slugs pack considerable short-range wallop, they are seriously lacking in sectional density (SD). Sectional density is defined as the ratio of a bullet's weight (in pounds) to the square of its diameter (in inches). SD matters because, other factors being equal, a long, thin projectile penetrates better than a short, fat projectile. When you think about it, that should be obvious.
Cutting to the chase, for stopping a bear you want a projectile with a high SD. Examples of common calibers and bullets that are recommended for shooting the great bears include the .30/220 (SD .331), .338/250 (SD .313), .35/250 (SD .279) and .45/350 (SD .238). By comparison, the common 12 gauge/437 grain (one ounce) rifled slug has a SD of only .117, which is woefully inadequate. (It is actually inferior to a 45 grain .22 bullet, which has a SD of .128!) For more on shotguns for protection in the field, see the article of that name on the Shotgun Information Page. However, for our purposes here, shotguns are out.
The rest of the article is here,
http://www.chuckhawks.com/firearms_defense_bears.htm