Heat a large nonstick skillet over medium heat. Add ground beef; cook and stir until browned, 5 to 10 minutes. Stir in black beans and red bell pepper; cook until heated through, about 5 minutes.
Cut four 13x13-inch pieces of aluminum foil.
Place 1 tortilla on each piece of aluminum foil. Spoon beef mixture in a line down the center of each tortilla. Divide cheese evenly among tortillas. Fold opposing edges of each tortilla to overlap the filling. Roll up in the shape of a burrito, sealing ends.
Rinse and dry 4 half-gallon wax-lined milk cartons. Cut several 1-inch diamond-shaped vents into 2 corners of each milk carton, near the bottom. Place a wrapped burrito inside each carton.
Place milk cartons in a safe cooking area outdoors. Light each on fire at one of the vents; cook until cartons burn down, about 2 minutes. Gently unwrap burritos with heatproof gloves.