In a small saucepan, bring 1 cup of the water to a boil. Place the bamboo shoots in a small heatproof bowl and pour 1/2 cup of the boiling water over them; let soak for 5 minutes then drain. Add the dried mushrooms to the water to the water remaining in the saucepan and let soak for 15 minutes. Drain the mushrooms through a sieve, reserving the soaking liquid. Slice the mushrooms, discarding the stems.
In a large saucepan, heat the oil over moderate heat. Add the chicken and sauté for 4 minutes or until no longer pink on the outside. Add the soaked mushrooms, fresh mushrooms, green onions, stock, soy sauce, honey, and mushroom soaking liquid. Bring the sauce pan mixture to a simmer.
Meanwhile, in a small bowl, mix the cornstarch with the remaining 1/4 cup water. Stir the cornstarch mixture into the simmering soup and cook for 5 minutes. Stir in the tofu, vinegar, and red pepper sauce. Cook until the tofu is heated through.