Cook udon noodles according to package directions; drain. Return noodles to saucepan; cover and keep warm.
Meanwhile, for sauce, in a small bowl stir together soy sauce, honey, oyster sauce, vinegar, cornstarch, and sesame oil; set aside.
Pour cooking oil into a wok or large skillet. (Add more oil as necessary during cooking.) Heat wok over medium-high heat. Stir-fry ginger and garlic in hot oil for 15 seconds. Add sweet pepper and green onions. Stir-fry about 2 minutes or until sweet pepper is crisp-tender. Remove vegetables. Add bok choy, half at a time; stir-fry about 3 minutes or until crisp-tender. Remove bok choy. Add tofu; stir-fry for 4 minutes. Push tofu from center of wok.
Stir sauce; add to center of wok. Cook and stir until slightly thickened. Return all vegetables to wok. Add cooked noodles and water chestnuts. Stir all ingredients together to coat with sauce; heat through. Serve immediately. Makes 4 servings.