Combine eggs, turkey bacon, mushrooms, onion, green bell pepper, red bell pepper, and Creole seasoning in a bowl. Stir egg mixture well to combine.
Heat a skillet over medium-low heat. Add oil. Pour egg mixture into the skillet. Cook until edges are dry, about 5 minutes. Flip omelet over. Place Cheddar cheese slices on top of the omelet and cook until set, 5 minutes more. Fold omelet over the cheese. Flip again and cook 2 minutes. Flip once more and cook until cheese is melted, about 2 minutes more.
Remove omelet from the pan and allow to sit for 1 minute to cool.