Place mushroom stems, orange bell pepper, onion, carrot, and bacon in a skillet over medium heat. Cook and stir until softened, about 5 minutes. Stir in 1 cup Cheddar cheese and sour cream; cook until stuffing is well combined and cheese has melted, about 2 minutes.
Preheat air fryer to 350 degrees F (175 degrees C).
Arrange mushroom caps on the baking tray. Add stuffing in a heaped fashion to each mushroom cap. Sprinkle 1 1/2 tablespoons Cheddar cheese on top.
Place the tray of mushrooms into the basket of the air fryer. Cook until cheese melts, about 8 minutes.