Whisk eggs together in a bowl; stir in bacon.

Melt butter in a skillet over medium heat. Add egg mixture; cook and stir until eggs are completely set, 2 to 3 minutes. Stir in American cheese, salt, and pepper.

Wrap tortillas in damp paper towels; microwave until warmed through, 30 seconds to 1 minute.

Spoon 1/4 cup egg mixture into the center of each tortilla; fold sides to cover. Serve with salsa.