Cut the chicken into 48 small cubes. Place in a bowl, pour in 1/3 cup teriyaki sauce and toss to coat. Marinate in the fridge for 2 hours. Make a dip by combining the mayonnaise, ginger and 2 Tbsp. teriyaki sauce in a small bowl; store in the fridge until needed. Preheat the oven to 425 degrees F. Thread 3 pieces of chicken and 1 green, and 1 red, bell pepper cube on each wooden skewer. Set on a parchment paper-lined baking sheet; drizzle any leftover marinade over top the chicken. Roast for 20 minutes, or until cooked through. Arrange on a platter with the dip and serve.