Preheat oven to 200 degrees F (95 degrees C). Wrap tortillas in aluminum foil; place in the preheated oven.
Cook bacon in a skillet over medium heat until browned, about 5 minutes. Remove bacon from skillet. Cook and stir refried beans in bacon grease until heated through, about 1 minute. Cover beans and remove from heat.
Whisk together eggs and egg whites in a bowl until uniform, about 1 minute. Heat oil in a skillet over medium heat, add egg mixture. Cook and stir until almost solid, about 2 minutes; stir in Cheddar cheese and remove from heat.
Top each warm tortilla with 2 tablespoons of refried beans, 2 bacon strips, half of the eggs, 1 tablespoon of salsa, and 1 tablespoon of sour cream. Roll tortillas into burritos.