Since unmanned bicycle robots have high mobility and do not require wide contact space to the ground, it is expected that they will be used as one kind of the robots working in disaster areas and/or in the mountains. We are developing one of the unmanned bicycle robot systems with a balancer and it can do a wheelie and move to track the path in the ground plane. In this paper, we propose a control strategy to perform an acrobatic turn with wheelie motion, which can be quick and require minimum contact space for a bicycle by using nonlinear control based on the output-zeroing controller. The dynamic models of the bicycle with the balancer are derived from Lagrangian's equations and they are combined by Lagrange's multiplier according to nonholonomic and holonomic constraints between subsystems. The effectiveness of the proposed method is shown by several numerical simulations using a detail model of a bicycle.