In 12-inch nonstick skillet, cook bacon over medium heat about 4 minutes, stirring occasionally, until almost cooked. Add onion. Cook 2 to 3 minutes, turning occasionally, until tender. Remove bacon and onion from skillet. Reserve 1 tablespoon drippings in skillet.
To make each sandwich, layer cheese, bacon and onion between 2 bread slices. Place 2 sandwiches in drippings in skillet. Cover and cook over medium-low heat 3 to 5 minutes, turning once, until bread is crisp and golden brown and cheese is melted. Repeat with remaining sandwiches.