In a large skillet over medium-high heat, sauté beef, bell pepper, and garlic in oil, stirring occasionally until beef is browned and vegetables are just tender.
Reduce heat to medium. In a small bowl, whisk soy sauce, vinegar, water, sugar, ginger, and cornstarch/water mixture until smooth. Add to pan and cook several minutes, stirring occasionally until sauce is slightly thickened.
Stir noodles into sauce mixture until evenly coated. Season with salt and pepper to taste. Top noodles with green onions and serve warm.