Most two-wheeled robots have algorithms that control balance by assuming constant contact with the ground. However, such algorithms cannot confer stability in robots deployed on non-continuous ground terrain. Here, we introduce BBot, a robot that can hop as well as move over stepped terrains. BBot has a two-wheeled lower body platform and a spring-loaded movable upper body mass. Hopping results from the impact force produced by release of pretensed springs. An inertia measurement unit detects the angle of body tilt, and an ultrasonic distance sensor records the height above ground. An accelerometer in the inertia measurement unit measures the impact force to determine the beginning and end of the phases of hopping and landing. Torque generated from rotation of the drive wheels controls the airborne robot's body angle. Sensors detect the impact of landing, and controls immediately switch to ground balance mode to stay upright. Experiment results show that BBot is capable of traversing down a 17 cm step, enduring manual toss landing and hopping 4 cm above ground.