"If" there's a 33 cal min for brown bears in Alaska, it's something "very" new, as there never was all the years i lived there!!
As for the origional cal question. The 30/06 with proper bullets will do all you need to do, but if i some how got magnumitis, i'd get a 7mm Rem mag.! With 175 Nosler partitions, it's up to the task of "any" animial in the U.S., includeing the big bears!!! In fact that combo will out penetrate most all the bigger common calibers with std expanding bullets. The 7 mag has less recoil than the 300 win. mag. too.
I figured out many years ago that i didn't need a magnum for any of my shooting needs, but a 7 Rem. mag. would be my magnum choise if i did.
Drilling Man