I carry a revolver whenever I am out and about. It is what I hunt with.
There is no problem using an across the chest style shoulder holster with a pack. I use a Bianchi 4100 Ranger nylon . Optics Planet has the best prices on these.
The nylon is not as pretty as leather, but is far superior for serious handgun carry here in Alaska. It is half the weight of any leather holster, and will not absorb moisture.
I have lots of nice leather holsters, but always use nylon for packing a heavy revolver. I have been carrying a revolver like this for over 45 years, so I have tried everything.
Also, I agree that technically a rifle of sufficient caliber is more desirable for bear defense, however there are lots of tales over the years of folks getting attacked and loosing touch with their rifle. A handgun is always with you and is better than sticking your hand down their throat!!
Bear spray is for folks that qualify for Natural Selection awards!!
A large caliber handgun, with a proper bullet, and in the proper hands is a very viable bear weapon. I have killed several brown/grizzlies with a .44, and have several friends that have done the same. Although I have to add that we are all experienced handgun hunters.
Bob