In a large bowl, combine the cooked shredded chicken, chopped bell peppers, ranch dressing, and half of the shredded cheddar cheese. Stir until the mixture is well combined and creamy.
Warm the flour tortillas in the microwave for 20 seconds or in a dry skillet for 10 seconds per side to make them pliable.
Lay the tortillas flat. Divide the chicken mixture evenly among the centers of the four tortillas.
Top the filling with the remaining shredded cheddar cheese.
Fold the sides of the tortilla inward over the filling, then roll tightly from the bottom up to enclose the burrito.
Optional: Place the burritos seam-side down in a dry skillet over medium heat. Cook for 2-3 minutes per side until golden brown and crispy.
Serve warm immediately with extra ranch for dipping if desired.