So one time I was out camping by myself and didn't bring a toothbrush or toothpaste (too much of a hassle). On this trip, I also had a summer sausage, which I ate before going to bed. In the morning, my breath stunk so bad that I was grossing myself out!
Here's a quick alternative to brushing your teeth while out backpacking. Go to your local Wally World and pick up one of the dollar travel mouthwash bottles. Rinse and spit in the morning, rinse and spit at night. It may not be as good as brushing, but it will kill those bacteria, and eliminate the breath that can stop a bear at 50 paces.
And when you return to civilization, you can always refill the bottle for your next excursion.