The non-reciprocity of energy transfer, particularly strong non-reciprocity, achieved within a wider range of excitation parameters, can enhance the performance of non-reciprocal devices. The influences of bistable elements on the energy transfer mode and the modulation of non-reciprocity are investigated. Initially, the dynamic equation for a system incorporating linear stiffness, cubic stiffness, and bistable components is derived. The semi-analytical solutions for this system are obtained using the complexification-averaging and least square methods. The numerical solutions are obtained via the Runge-Kutta method. Then, the accuracy of the analysis procedure is confirmed through a comparison of semi-analytical and numerical solutions. Building on this, the non-reciprocal characteristics of the system under harmonic excitation and the effects of excitation amplitude are analyzed. The results show that regardless of the presence of the bistable component, the nonlinear system undergoes a transition from the reciprocal to a non-reciprocal state and then back to the reciprocal state. However, the bistable component significantly alters the non-reciprocal characteristics. Furthermore, it is found that an appropriate negative stiffness in the bistable system can effectively decrease the excitation amplitude threshold for activating the non-reciprocal state.