With an '06 I would limit my shots to 350 yards. That's when the '06 starts to give up too much ground to the Mags. Use a stout bullet designed to penetrate, NOT a plastic tip varmint bullet loaded in Big Game Calibers (SST< Ballistic Tip).
Use a Fail Safe, Barnes X, Trophy Bonded Bear Claw, Swift A Frame, or any BONDED bullet in 165-180gr, and you should be just fine.