Form beef into eight, thin, 4-inch patties. Place softened Bleu Cheese on top of four patties and cover with another patty. Seal edges of patty with hand.
Place burgers on a hot grill and cook for 3 to 5 minutes on each side, or until degree of doneness is achieved. Grill buns or bread slices on top rack until lightly toasted. When ready to serve, place each burger on a toasted bun or bread slice. Top with tomato and onion slices and enjoy. Top with two slices of cooked bacon.