There was a penetration test on here somewhere...30 cals of all sorts against 6" cow femur and then a medium to simulate tissue. Based upon that test alone, I'd not worry about Bergers being too "soft" to get through a bear skull. If you read the writings of the guy who started Buffalo Bore Ammo, he has a lot to say about putting bears down, and what is actually required from his experience. I hunt where there are bears, and I don't in the slightest feel under-gunned for bear attack with Bergers, though it does sound like there may be a bit more likelihood for you to see some in action, OP. Above all, carry what gives you confidence, as that will help you do what needs doing should the need arise.
Years ago I learned to "pick my experts" when it came to things of which I knew nothing at all.... Generally this has worked out well.
So when it comes to VERY long range rifle shooting (not the common stuff like 400-500 yards) I will listen to John Burns,and use what he says works.
And when it comes to large,potentially dangerous animals like Alaskan Brown bears and grizzlies at spitting distance, I will listen to people like Phil Shoemaker and others who have BTDT numerous times,and take his advise,and use something like a Partition as a baseline,going "up" from there.
At the same time,f we think such bullets are a handicap on that 500 yard elk,we are sorta....uh....mistaken.
I certainly agree with you, Bob. Even out of a 308, a 180 partition should do fine on elk to 500yds, and would fit in with the Shoemaker approach to bear bullets. I submit that there are others who have killed lots of bears too, who also add to the common knowledge. I don't believe in any one man as the sole authority on anything, so I read what I can get my hands on, and try things for myself if I want some empirical data.
Obviously, with big, dangerous beasts, there is no such thing as too dead, especially at spitting distance, but the question that was originally posted was framed around Bergers against bears, since that is what would be in the hunter's 308 already. I know the standard line here is 'use a tougher bullet, and a bigger caliber', but what specifically about the OP's setup won't do the job?
Generally this has worked out well. 
