Cook bacon in a large skillet over medium heat until browned and crisp. Using a slotted spoon, remove bacon to a plate and set aside. Reserve drippings.
Add mushrooms and onions. Season with salt and pepper to taste. Saute, stirring frequently, onions are tender and mushrooms are soft, about 7-10 minutes.
Add bacon back to the skillet. Pour in barbecue sauce and stir until mixture is coated with the sauce and heated through.
Heat a separate 10-inch skillet over medium heat. Spread half of bacon mushroom mixture over one tortilla. Sprinkle with half of the cheese. Top with a second tortilla.
Heat quesadilla until tortillas are browned and cheese is melted, about 5-7 minutes, turning once during cooking.