I like the comments better than the article.
If I was unfamiliar with firearms I would be packing the same thing that she was. Also the article says that the bear approached from behind her and that she didn't hear it coming. I highly doubt that she or just about anyone else could of gotten a firearm out of a holster to of done any good. She did manage to unholster her bear spray and after spraying the bear and herself the bear went away.
So other than the initial attack the bear left her along after getting a dose of the spray, so there is no real need to kill the bear and if she were to of shot it with a handgun odds are that would of just made the bear mad.
It's impossible to claim that the spray did it's job because none of us can prove that it did or didn't, nobody can tell what would have happened if she didn't use the spray, the bear might have stayed and killed her or it might have done exactly what it did do - walk away. Bears don't always kill when they attack people, in fact, more often than not they maul you and then walk away, and that's what this bear did, I see nothing to prove that the spray did anything except give her more pain and discomfort.
I also disagree with your assumption that she had no time to draw a gun, if she had time to draw the spray then she had time to draw a gun, as a matter of fact, a gun is retained in a holster that is designed to allow the gun to be drawn quickly, sprays are stored in cheap nylon bag-like holders that aren't easy to draw from so I'd bet that the gun could have been drawn quicker than the spray.
But the more important point is that if she had time to draw that spray then why did the bear hurt her? I suspect that the fact is that she drew that spray before or just as the bear hit her because I find it hard to believe that once the bear started slashing and biting her she could have gotten her hands to the spray, pulled it from the holder, disengaged the safety, and deployed it. I'd bet that if the truth were known then you'd find out that the she drew the spray and deployed it just as the bear hit her, it was so close at that time that the spray's cloud engulfed her and the bear but it didn't stop the bear at all, it simply made her life more miserable and when the bear was done doing what it intended to do it walked off.