Electric Vehicle (EV) bidirectional charger technology is growing in importance. It defines the fact of returning the electricity stored in the batteries of EV to Grid (V2G), to Home (V2H), to Load (V2L), or in one word V2X mode. The EV onboard charger is divided into two parts: AC-DC and DC-DC converters. The isolated bidirectional DC-DC LLC resonant converter is used to improve the charger efficiency within both battery power and voltage ranges. It is controlled by varying the switching frequency based on a small signal modeling approach using the gain transfer function inversion method. The dimensions of the DC-DC LLC converter directly affect the charger cost. Moreover, they cause an important control frequency saturation zone, especially in V2X mode, where the switching frequency is out of the feasibility zone. The new challenge in this paper is to design an optimization strategy to minimize the LLC converter cost and improve the control frequency feasibility zone, for a wide variation of battery voltage and converter power, in the charging (G2V) and discharging (V2X) modes simultaneously. For our best knowledge, this optimization problem, in the case of a bidirectional (G2V and V2X) charger, is not yet considered in the literature. An optimal design that considers the control stability equations in the optimization algorithm is elaborated. The obtained results show a significant converter cost decrease and important expansion of control frequency feasibility zones. A comparative study between initial and optimized values, in G2V and V2X modes, is generated according to the converter efficiency.