ECO-DENT toothpowder. Use it in my day to day life, and it's also perfect for the back country as it's lighter and easier to transfer than paste.
I brush away from camp to avoid attracting critters, and away from any water sources because, eww. Disposal method could range from moving aside and replacing duff to digging a cat hole, depending on the environment. Another benefit to tooth powder is that it doesn't create as much froth, and the residue is easily diluted.
Pro-tip (or possibly just disgusting suggestion): After brushing but before rinsing my toothbrush, I use it to clean my eating utensils.