Since your question was regarding a 30-06 on black bears and not a .50cal muzzle loader.....I'll stick to the topic for yas...

Your 165gr core lokt is plenty medicine for black bears, no matter how big. As Big country said, his buddy used a .243. Now, I wouldn't because I'm not that good with shot placement. However, i've taken in excess of half a dozen black bears with a 150grain 30-06 bullet. The furthest range I shot one was about 350yards. Hit him in the spine and blew out the bears "rear wheel drive" (rear legs, couldn't move them). A second shot was higher up and took him out in the lung area where he died seconds later. Im confident that had my 1st shot been placed higher, I would have got him without having to use a follow up shot. I was shooting down a steep mountain and forgot about bullet trajectory and aiming low etc...

To illustrate that your '06 with the 165's are perfect, I've killed a few bears in my life time with wimpy old 30-30 loads and 150grainers and 170 grainers. Not nearly the amount of energy of a 30-06.

Have fun with yer '06 and hope you get a bear.