Combine the marinade ingredients together in a bowl, add the chicken breast and toss to coat. Set aside to marinate at room temperature while you julienne the vegetables and prepare the "toppings".
Heat a small amount of oil in a wok or large sauté pan over medium-high heat; add the chicken and cook for 2 - 3 minutes or until cooked through. Remove from the wok and set aside. Wipe the wok clean
Add a bit more oil and add the garlic, ginger, red bell pepper and carrot, cook, stirring often for about 2 minutes or until crisp-tender, return the chicken to the wok along with the bamboo shoots; stir in the sauce and stir until well combined. Turn off the heat and allow to sit for 5 minutes so it's not super hot when you put it into the lettuce cups.
Take 1 or 2 bibb lettuce leaves; fill with 2 or more tablespoons of the filling, then add toppings of your choice. Fold, taco-style, and enjoy.