Soak mushrooms in hot water 20 minutes or until soft. Drain. Rinse in warm water. Drain. Squeeze out excess moisture. Remove and discard stems. Chop caps finely. Mix together mushrooms, pork, bamboo shoots, green onions, egg white, cornstarch, salt, 2 teaspoons soy sauce, 1/2 teaspoon sesame oil and white pepper.
Hold siu mai skin in hand. (Cover remaining skins with plastic wrap to keep them pliable.) Place 1 tablespoon pork mixture in center of skin. Bring edge of skin up side of filling, leaving top open.
Repeat with remaining skins. (Cover filled dumplings with plastic wrap to keep them from drying out.) Place dumplings in single layer on rack in steamer. Cover and steam over boiling water 20 minutes. (Add boiling water if necessary.) Repeat with remaining dumplings. Mix together 1/4 cup soy sauce and 1/8 teaspoon sesame oil. Serve with dumplings. NOTE: Wonton skins can be substituted for siu mai skins. Cut off corners to make a circle.