Preheat oven to 375 degrees F (190 degrees C). Arrange bacon on a baking sheet.
Bake in the preheated oven until just crisped, 10 to 12 minutes.
Beat eggs and water together in a bowl.
Let the bacon cool on paper towels, about 5 minutes. Break into small pieces.
Spray a 10-inch non-stick skillet with cooking spray. Melt butter over medium heat until foaming, about 2 minutes. Add onion once butter is no longer foaming. Cook and stir until tender but not browned, 4 to 5 minutes.
Increase heat to medium-high. Pour eggs into the skillet and cook until mostly set, about 2 minutes. Lift the omelet with a spatula as the center rises; tilt the skillet so that uncooked eggs run to the center of the pan. Cook until set, 2 to 4 minutes. Sprinkle bacon pieces onto the omelet and fold in half using the spatula.