In a nonstick pan on medium low heat cook the bacon on both sides until it is crisp.
Lightly toast the bagels.
Heat the oil in a nonstick pan on medium heat. Crack the eggs into the pan, season with salt and pepper. Cook until top is nearly set but still glossy, then flip the eggs over, add the sliced cheese and melt.
Place the eggs on the bagel, cut in half and serve with oranges.