Keith Rogan, who survived a bear mauling, has posted here numerous times. His advice is that a .44 Mag is marginal to useless if the bear is actually charging. Self-defense against bears is best done with something like a .45-70 Guide Gun and Garrett loads.
While some hunting guides will accept a skilled hunter with an '06 and heavy bullets, I'm of the "more is better" school--from many years of reading, going back to Russell Anabell's stories. (Annabel?) I'd most likely go with a .338 or .375.
Purely opinion,
Art