I'm thinkin' the best 44mag would be S&W 500 
I don't have one, but I have a bunch of 44's so I'm definitely not knockin' 'em...

I don't have one, but I have a bunch of 44's so I'm definitely not knockin' 'em...
In a grizzly charge scenario you are probably not going to get off six rounds, let alone 15. I suppose it all comes down to what you feel comfortable with.
Woo hoo! Bear thread!
This guy’s trusty .357 Smith worked for him.
Montana Grizzly Attack Caught on Camera | Field & Stream
...I had a close encounter with an angry black bear. Long story shortened I almost shot him through the ear, but he backed off after a 30-minute face-off.
You have been given several good suggestions but I would say that the best 44 mag for this purpose would be the Ruger Super Redhawk Alaskan.
Personally, I would try and find a M629 Mountain Gun, which is a stainless .44 Magnum with a tapered barrel. Carry it with the stoutest load you can handle well.
Another vote for 4.25 inch model 69. I remove the lock on mine as years ago I had 329pd self lock 2 times on me. I doubt it would be a problem with a steel frame however since you do not get the significant frame flex that you get with aluminum frame guns. I did it anyway to make me feel better.