Hi, I wasnt on this forum quite a while.
I wouldnt use 308 on the bear in walk and stalk, or accidental meeting & selfdefence scenario, and given the circumstances I would opt at least for any other option, like renting a more appropriate rifle, or buying such rifle.
But to keep in line with thread, I would suggest:
Hornady superperfomance ammunition which can squeeze out additional 100 to 200 ft/sec, as per manufacturer claims. In some elaborations it is more powerful then average 30-06.
The bullet to be used, as hard as possible, for controlled expansion and maximum penetration, such as:
interbond
or GMX
Keep in mind that charging bear is full of adrenaline, and even good hit in vital organs will probably not stop him. Hitting cns should stop him in his tracks, only.
It is different if using same caliber for aimed shot, from a stand for example and effectiveness of same caliber in different situation is completely different.
However, using a rifle in 308 on a bear, is also a better option then using a handgun...
Good luck!