Spray 2 skillets with cooking spray. Heat over medium.
Add bacon to one skillet; cook until crispy and no longer pink. Place on a plate lined with paper towels to cool.
Meanwhile, dice pepper, onion, and mushrooms; toss into a bowl and set aside.
In a separate bowl, whisk together 1 whole egg and 2 egg whites. Pour into second skillet and sprinkle with 1/4 of the veggies. Cook until eggs begin to set. Swirl skillet so that the eggs begin to move around and cook. Flip eggs over and cook until no longer runny. Fold omelet and place inside a roll along with 2 pieces of bacon. Continue until all sandwiches have been prepared.