The 30-06 is the single most versitile round ever made,every gun made after the 30-06 was made to beat or duplicate it's performance.
It has good BC and SD also good range and power.You realy don't need anything else in the Ol' gun cabinet if you have a "06,but what a boring world it would be.
I would not hesitate to shoot a Griz,Polar bear or Moose with the 30-06,shooting 220gr. or 180 gr. bullet you should be good.

If I was going where the chance of meeting a hungry bear,I would op for bigger,300 WSM,300 Win Mag or my favorite 338 Win Mag.