In my opinion, the question shouldn't be "am I responding to a lethal threat in a non-lethal manner" but rather "am I responding to a lethal threat in the manner which provides me the best chance of survival." My goal when facing such a threat should be to end the attack as quickly as possible without experiencing injury or death (my own, that is!).

Looking at the studies available (at least the ones I've found), the evidence suggests that you are more likely to be injured or killed if you defend yourself against a bear using a firearm as opposed to bear spray. For example:

Law enforcement agents for the U.S. Fish and Wildlife Service have experience that supports this reality -- based on their investigations of human-bear encounters since 1992, persons encountering grizzlies and defending themselves with firearms suffer injury about 50% of the time. During the same period, persons defending themselves with pepper spray escaped injury most of the time, and those that were injured experienced shorter duration attacks and less severe injuries. Canadian bear biologist Dr. Stephen Herrero reached similar conclusions based on his own research -- a person’s chance of incurring serious injury from a charging grizzly doubles when bullets are fired versus when bear spray is used.

Based on all I've read, I now advocate that the best form of defence against a bear attack (black or grizzly) is bear spray. I won't tell people they shouldn't carry guns, but at the same time I would not recommend a firearm as someone's primary defensive tool against bears.