Here are some of Andy's tips on photographing brown bears:
Exposures are actually very very difficult for most, so here is how I approach shooting the bears.
Always shoot on manual if you have slow changing light. Especially overcast light.
Watch out for highlights on their backs, as their hair gets lighter the farther away from their body. So you will see the lightness more on their backs than anywhere else.
Take a shot. Check your histogram!!!! Everything else can be perfect, but you will get specular highlights blowing out. This is a major pain.
I tend to underexpose a little bit to keep the highlights in check, but the overall scene is slightly under exposed. This doesn't happen in overcast situations, though, and you will have to use positive exposure compensation as a result.
Be sure to check with your tour leader to see how he specifically deals with exposures. I rarely use anything other than evaluative metering in situations such as this.
Most everything in the scene in middle toned, at least when they are grazing, so I just start from there.
If you are looking to improve your photography, make sure to check out one of Andy's awesome photography workshops.