It is important to accept the limitations of the weapon you choose to hunt with. Be it rifle, handgun, long bow, crossbow, or spear. If that limitation is a perfect broadside shot so be it.
But, do recognize that limitation. A pistol is not the weapon to use for a raking shot, nor is an arrow, but if you have a .338 Win Mag to shoulder why not? This forum is as good a place to get advice on the limitations of a particular load as any.
To think a 25-06 has less killing power than a .44mag pistol is a foolish position. A .44 mag pistol is often touted as a perfectly acceptable choice, because one assumes the person knows it is a short range proposition, and has accepted that limitation. Accepting that a .25 bullet is not generally built to break heavy bone and drive deep does not mean it can't be very deadly on that bear. Treating like it is a .338 WM or a .45-70 is wrong, just like an archer trying the same thing would be wrong.
It'll work just fine, work within its design capabilities, choose a good heavy strong bullet. Learn the anatomy of a bear, and the shooting characteristics of you rifle. Bears aren't armored, but they are well constructed from the diaphram forward when compared to deer, shoot accordingly.