The backswimmer fly is an aquatic insect, capable of regulating its buoyancy underwater. Its abdomen is covered with hemoglobin cells, used to bind and release oxygen, reversibly. Upon entering water, the fly entraps an air bubble in a superhydrophobic hairy structure on its abdomen for respiration. This bubble, however, can change its volume through regulated oxygen flow from the abdominal hemoglobin cells. In this way, it can reach neutral buoyancy without further energy consumption. In this study, we develop a small, centimeter scale, backswimmer inspired robot (BackBot) with auto-buoyancy regulation through controlled nucleation and release of microbubbles. The bubbles nucleate and grow directly on onboard electrodes through electrolysis, regulated by low voltage. We use 3D printing to introduce a three-dimensional bubble-entrapping cellular structure, in order to create a stable external gas reservoir. To reduce buoyancy forces, the bubbles are released through linear mechanical vibrations, decoupled from the robot's body. Through pressure sensing and a Proportional Integral Derivative control loop mechanism, the robot auto-regulates its buoyancy to reach neutral floatation underwater within seconds. This mechanism can promote the replacement of traditional and physically larger buoyancy regulation systems, such as pistons and pressurized tanks, and to enable the miniaturization of Autonomous Underwater Vehicles.