Dissolve yeast in warm water; let stand 5 minutes. Combine buttermilk, flour, mashed potatoes, and sugar in a medium-size nonmetal bowl; mix well. Add yeast mixture, and stir until well combined.
Cover loosely with plastic wrap or cheesecloth, and let stand in a warm place (80° to 85°) for 12 hours.
To use, stir well, and measure amount of starter needed for recipe. Replenish remaining starter with 3 parts flour to 2 parts water and 1 teaspoon sugar. For example, if 1 1/2 cups starter is used, add 1 1/2 cups flour, 1 cup warm water (105° to 115°), and 1 teaspoon sugar. Stir until blended.
Stir in 1 teaspoon sugar daily when not used to keep starter active.