I would never shoot a bear with something I thought "might" effectively stop it. The chances are greater that you're just going to **** it off and get torn to shreds in the process.
I'd say .44 mag is the minimum I'd be willing to sting a bear with, black or grizzly.
Small black bear killed by home owner on the stairs in his house as it started up towards the bedrooms last year with a .40 S&W, think it was a JHP. Lung shot as I recall, So can work. Not for Brownies though!!!