Place bacon in a skillet over medium heat; cook until crisp, about 10 minutes. Lay on a paper towel to absorb excess grease. Crumble cooled bacon into bits.
Flatten white bread with a rolling pin. Coat chicken in Buffalo sauce.
Place 1 tablespoon butter in a microwave-safe bowl; heat in microwave until melted, about 30 seconds.
Place chicken strips onto the flattened bread; sprinkle a small amount of bacon bits and mozzarella cheese on top. Coat the opposite side of the bread with melted butter; roll up the bread, securing the chicken inside the roll-up.
Heat remaining butter in a skillet over medium heat. Fry the roll-ups in batches until bread is toasted, 2 to 3 minutes.