FOR THE STIR-FRY: Move oven rack to lowest position, place large rimmed baking sheet on oven rack, and preheat oven to 500 degrees F.
In large mixing bowl toss chicken, mushrooms, bell peppers, pineapple, oil, 2 teaspoons of the garlic, and 1 ½ teaspoons of the ginger together. Season with salt and pepper.
Work quickly to spread chicken mixture in an even layer on hot baking sheet. Roast until chicken is just cooked through, and vegetables and pineapple begin to brown, about 10-12 minutes, stirring halfway through roasting.
FOR THE TERIYAKI SAUCE: Meanwhile, in large microwave-safe bowl whisk together mirin, soy sauce, water, brown sugar, cornstarch, red pepper flakes, remaining 1 teaspoons garlic, and 1 ½ teaspoons ginger. Microwave sauce on high power, whisking occasionally, until sauce has thickened, 4-5 minutes. Stir bamboo shoots into hot teriyaki sauce, and cover to keep warm until needed.
Transfer roasted chicken, vegetables, and pineapple to bowl of teriyaki sauce and toss to combine. Serve over white rice, sprinkle with green onion, and serve.