A 30.06 will work great! Are you going to carry it on your back with a sling or in the front? When I'm hunting a rifle is all the protection I need but it is very accessible.

Even though the 30.06 is good medicine for black bears, it is not realistic to have one on your person 24/7.

If you are in real bear country with a real threat, the only way to fully protect yourself, is to have your protection with you at all times.

I'd choose a .357 minimum but I would probably have a 44 mag on my hip. Keeping bear spray close by would also be a good choice.