In a large skillet over medium-high heat, heat olive oil. Add peppers and onion and season with salt and pepper. Cook until soft, 5 minutes. Transfer to a plate.
Heat remaining tablespoon vegetable oil over medium-high heat. Season chicken with spices, salt, and pepper and cook, stirring occasionally, until golden and cooked through, 8 minutes. Transfer to a plate.
Preheat oven to 350 degrees F (175 degrees C).
Layer half of each tortilla with the chicken and vegetable mixture, then sprinkle with the Cheddar cheese, bacon bits, and Monterey Jack. Fold the tortillas in half and Place onto a baking sheet.
Bake quesadillas in the preheated oven until the cheeses have melted, about 10 minutes.
Slice into wedges and serve with sour cream.
