In a small microwave-safe bowl, microwave the beans and rice until hot, about 2 minutes. Mix well.
Meanwhile in a large nonstick skillet heat the oil over medium-high heat. Add the green pepper, salt and pepper; cook until crisp-tender, about 5 minutes. Add the eggs to the skillet and cook until the edges set, then gently pull in the edges with a rubber spatula. Repeat until the eggs are cooked through, about 3 minutes.
Microwave the tortillas according to the package's directions until pliable. Divide the bean mixture among the tortillas and top with the egg mixture, avocado, and cheese. Roll up the tortilla. If desired, serve with salsa.