Melt the butter over medium heat in a large skillet. Add the onion and bell pepper; cook and stir until the onion is transparent, 5 to 7 minutes. Stir in the mushrooms and bacon, and cook 2 minutes more. Remove skillet from heat, and place the vegetable-bacon mixture in a bowl.
Pour the eggs into the same skillet. Cook and stir gently just until the eggs are soft. Stir the vegetable-bacon mixture into the eggs. Season with salt and pepper. Cook the eggs until firm. Remove skillet from heat and stir in the tomato and cheese. If desired, stir in the ketchup.
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