In a large heavy skillet, cook bacon over moderate heat until crisp. Remove and drain. Pour off all but about 3 tablespoons of bacon drippings. Heat drippings in the pan until sizzling. Add the green pepper, onion, and potatoes; cook, stirring gently, until the potatoes are browned. Sprinkle on the shredded cheese and stir until melted. Add the eggs and cook, stirring gently, until eggs are set. Season with salt and pepper. Sprinkle on the crumbled bacon and serve at once.
Serves 4 to 6.