If you live in a state where hunting bear with dogs is still allowed, the barking dog might work. Most states banned this practice years ago, so in most places, fear of dogs is no longer instilled in bear (or cougar).

The most common scenario with dogs and bear: Unleashed dog is allowed to run ahead of owner. Dog sees bear. Dog runs up to bear barking. Bear gets mad and chases dog. Dog makes hurried retreat to owner for protection with angry bear in hot pursuit. This can happen not only with bear but with elk, moose, cattle, even deer. Good luck if that happens!

Actually, dogs are allowed in most wilderness areas in national forests, but not anywhere off the pavement in national parks. Leashes are required in some areas and are a good idea everywhere--to keep the dog from getting into a dangerous area (like the crumbly edge of a cliff), to prevent the dog from threatening other hikers (even the sweetest, friendliest dog can become fearful and over-protective in a strange place), to prevent the dog from chasing wildlife, to prevent him from "going" on a possible campsite, etc. Unless your dog is so thoroughly trained that he will always come to you immediately the first time called, no matter what distractions are around, even a running rabbit, he should be on leash. Your fellow-hikers will thank you. Barking dogs are a considerable annoyance to others camping in the area, too! Please don't let your dog indulge in activities that will contribute to the prevailing anti-dog attitude among many hikers--the result will be the banning of all dogs!

As mentioned above, the dog is not going to protect you from much; you'll need to protect the dog!