In general, I wouldn't recommend it, although it would probably be alright for a short trip.

First of all, a bear has no fear of a dog, and they aren't really going to be too deterred. The fact that you are making any noise will let the bear know you are there, and should encourage it to go away, so it would be a slight benefit.

In the event of a close encounter, if a pet is let to go free, they might treat the bear like they would a human, getting close and barking. Well, that would be a very poor strategy for a bear, likely resulting in serious injury to the dog. Likewise, if you were to tie them up, it would likely lead to trouble if a bear should come in the camp.

I would say for a few hours, it probably wouldn't hurt, especially if you are in black bear country. If you are in Grizzly Bear country, or on an extended outing, or just want to be safe, leave the dogs home.