For Sauce: While fish is steaming, combine sauce ingredients in a small saucepan. Bring to boil over medium-high heat and cook, stirring until sauce thickens slightly.
Fish: In a bowl, soak mushrooms in warm water to cover until softened, about 15 minutes; drain. Discard stems and cut each cap into 3 slices.
Prepare a stir-fry pan for steaming.
Cut tofu into 4 pieces and place in a heatproof dish.
Arrange fish, mushrooms, and bamboo shoots over tofu. Sprinkle with ginger, salt and pepper.
Arrange bok choy around outside of fish.
Place dish in stir-fry pan, cover and steam over high heat until fish turns opaque and just begins to flake, about 7 minutes.