ChuckHawks has an interesting article on this subject. The 30-06 with 180-220 grain bullets is the minimum. If you cannot shoot anything heavier accurately use the 30-06. A gut shot bear with a 458 mag is not going to get the job done. He goes on to say that " In a survey taken a few years ago, it was found that the most popular caliber with Alaskan professional hunters and guides responsible for "backing-up" their clients was the .338 Winchester Magnum. With typical factory loads using 225 to 250 grain premium bullets the .338 Win. Mag. has a ME of about 3860-4046 ft. lbs. and a maximum point blank range (+/- 3") of about 270 yards. These can be taken as ideal ballistics for hunting any of the great bears. Recoil energy runs about 34 ft. lbs. in an 8.5 pound rifle."
http://www.chuckhawks.com/grizzly_cartridges.htm
http://www.chuckhawks.com/grizzly_cartridges.htm