This paper focuses on the control of bidirectional power flow in the electric shipboard power systems, especially in the Medium-Voltage Direct Current (MVDC) shipboard power system. Bidirectional power control between the main MVDC bus and the local zones can improve the energy efficiency and control flexibility of electric ship systems. However, since the MVDC system contains various nonlinear loads such as pulsed power load and radar in various subsystems, the voltage of the MVDC and the local zones varies significantly. This voltage variation affects the control performance of the bidirectional DC-DC converters as exogenous disturbances. To improve the control performance regardless of uncertainties and disturbances, this paper proposes a novel controller design method of the bidirectional DC-DC converters using $L_1$ control theory and intelligent optimization algorithm. The performance of the proposed method is verified via large-scale real-time digital simulation of a notional shipboard MVDC power system.