Preheat grill or grill pan over medium-high. Season chicken; grill 4 to 6 minutes per side. In saucepan over low, whisk next 5 ingredients until warm, 2 minutes. Toss all but 3 tbsp. sauce with noodles and bell pepper, adding enough pasta water to moisten. Slice chicken; serve over noodles and drizzle with reserved sauce.