Combine first 4 ingredients in a medium bowl, stirring with a whisk. Combine beans, onions, cheese, and salsa in a medium bowl.
Heat a medium nonstick skillet coated with cooking spray over medium heat. Pour egg mixture into pan; let egg mixture set slightly. Tilt pan and carefully lift edges of omelet with a spatula; allow uncooked portion to flow underneath cooked portion. Cook 3 minutes; flip omelet. Spoon bean mixture onto half of omelet. Carefully loosen omelet with a spatula; fold in half. Cook 1 minute or until cheese melts. Slide omelet onto a plate; cut in half.