Heat the olive oil in a medium nonstick saucepan over medium heat. Add the mushrooms for 3 minutes. Stir in the tomatoes and cook for 2 minutes. Transfer to a bowl and set aside.
Wipe out the skillet and set over medium heat again. Pour in the egg mixture and cook until the eggs are scrambled, stirring occasionally. Season with salt and pepper.
Stir the mushrooms, tomatoes and bacon in the eggs.
Place tortillas on 2 plates and spoon half of the egg mixture down the center of each tortilla, leaving room at one end. Sprinkle the basil over the egg.
Fold in the end, then roll up the tortillas. Serve.