Heat the oven to 375°F and grease a 9-by-13-inch dish. Cook the bacon in a skillet until crisp, drain and set aside.
Brown the beef and onion in the same skillet. Drain the fat and stir in tomato sauce, ketchup, mustard, Worcestershire, salt and pepper; simmer for 3 minutes.
Spread the hot beef mixture in the dish and sprinkle with bacon and 1 cup cheddar.
Arrange the biscuit quarters in one loose layer over the filling and sprinkle with the remaining cheese.
Bake for 30 to 35 minutes, until the biscuits are deeply golden and cooked through. Rest 10 minutes before serving.