Put some 180's in the 06 and it'll be fine if thats what you got. I do a lot of back packing, fishing and hunting in griz country here and use an 06, but I like my 870 loaded with slugs because its easier to pack than a rifle in. I also carry a can of pepper spray and a 357, 3" ruger on me at all times when deep in griz country. Just beware of your surroundings at all times and look for signs when in bear country.
Bobby