In a large resealable plastic bag, combine the egg white, soy sauce, cornstarch and pepper. Add chicken; seal bag and turn to coat. Refrigerate for 30 minutes. For sauce, combine the cornstarch, vinegar, soy sauce and sugar until smooth; set aside.
Drain chicken and discard marinade. In a large skillet or wok, stir-fry chicken in 1 tablespoon oil until no longer pink. Remove and keep warm.
Stir-fry green pepper and onions in remaining oil for 2 minutes. Add bamboo shoots and ginger; stir-fry 3-4 minutes longer or until vegetables are crisp-tender.
Stir sauce mixture and add to the pan. Bring to a boil; cook and stir for 2 minutes or until thickened. Add chicken and heat through. Sprinkle with almonds. Serve with rice if desired.