In a large skillet, cook bacon over medium heat until crisp. Remove to paper towels; drain. Crumble bacon and set aside.
Add the potatoes, onion and green pepper to drippings. Cook and stir over medium heat for 7-10 minutes or until potatoes are lightly browned and vegetables are tender.
In a large bowl, whisk the eggs, milk, salt and pepper. Pour egg mixture into a large non-stick skillet (mixture should set immediately at edges).
As eggs set, push cooked edges toward the center, letting uncooked portion flow underneath. When the eggs are set, spoon potato mixture on one side and sprinkle with cheese and bacon; fold other side over filling. Invert omelet onto a plate to serve.