Combine 1 cup boiling water and mushrooms in a bowl; cover and let stand 15 minutes. Drain mushrooms, reserving 2 tablespoons soaking liquid. Discard mushroom stems; thinly slice mushroom caps, and set aside.
Heat oil in a wok or large nonstick skillet over medium-high heat. Add mushrooms and bamboo shoots; stir-fry 2 minutes. Add reserved soaking liquid, snow peas, salt, and sugar; stir-fry 2 minutes.