I recently answered this question for deer, and I will re-post my answer from my web log:
What's the best 30-06 Ammo?[/url]
However, you're also talking bear. Bear is a bit tougher. The answers will be different. As you can see, I had years of experience with 180 grain. I would not feel under-gunned with 165 to 180 grain bullets. The answer is also dependent on the size of the bear.
I have not done bear-- not yet. So let me take you through the decision process I would go through. Essentially, it would be the same as what I said about deer. If we're talking small bear at normal forest ranges (under 100 yards), end of story. Go have fun. Lots of bear are done in with 30-30, and your rig is way beyond that.
If you know that you are hunting bigger bear and longer shots, I would be looking at a premium bullet for the bear. 150-180 grain will still be sufficient. On the other hand, I mention in the piece I did on whitetails that I once saw a cheese-ball 180 grain go end to end on a whitetail, plowing through a bunch of bone on the way. That was probably 3 feet of animal. If I could keep that idea in my head, I would be a lot happier and my wallet a lot heavier.
So now I'm back to green-box Wally World specials in 180 grain and using the difference of 30 grains over the 150 grain basic whitetail load as my insurance policy. But then I get this nagging thought: this may be the trip of my life, I want the best. Now I'm back scouring the mags and hitting all the websites and . . .
The bottom line is that probably all the mental gyrations are for naught. Again, if you really pick it apart, there are plenty of folks killing bear with stuff that has far less oooph than your Ought-Six. If you have one rifle and one trip, you won't go wrong going the premium route in either 165 or 180. Find the one that works best in your rifle and buy a few boxes. The premium bullet on the deer is a waste, and it's mental assurance on the bear. I would concentrate on killing the bear, and whatever does him in will be wickedly awesome overkill on the deer.
Now if it were me going with what's in my rack, I would be going with two rifles and two loads. I'd have my Remington 7600 in 35 Whelen and 250 grain Nosler Partitions for the bear and my Savage 99 in 308 Win with 165 Grain Hornady SP's for the deer. Each would back the other up. If it were one trip and one rifle, I'd probably redo the 165 grain 30-06 load using Hornady Interbonds. The premium bullets would just be there to kill doubt in my mind.