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Bikebot (i.e., bicycle-based robot) is a class of underactuated balance robotic systems that require simultaneous trajectory tracking and balance control tasks. We present a tracking and balance control design of an autonomous bikebot. The external-internal convertible structure of the bikebot dynamics is used to design a causal feedback control to achieve both the tracking and balance tasks. A balance equilibrium manifold is used to define and capture the platform balance profiles and coupled interaction with the trajectory tracking performance. To achieve fully autonomous navigation, a gyrobalancer actuation is integrated with the steering and velocity control for stationary platform balance and stationary-moving switching. Stability and convergence analyses are presented to guarantee the control performance. Extensive experiments are presented to validate and demonstrate the autonomous control design. We also compare the autonomous control performance with human riding experiments and similar action strategies are found between them.