Spread each bagel half and lightly grill or toast.
In a large pan, cook bacon over medium heat until crisp. Using a slotted spoon, remove to paper towels; drain, reserving 3 tablespoons drippings. Heat drippings over medium-hot heat. Add eggs; reduce heat to low. Fry until white is completely set and yolk begins to thicken but is not hard.
Place an egg on each bagel bottom. Layer with cheese slices, bacon and bagel tops.