It is able to achieve novel properties of vibration transmission by utilizing the nonlinear effects of metastructures. Bistable metastructures are known to possess the nonlinear supratransmission behavior, which states that in the linearized bandgap of metastructures, the transmitted vibration energy increases sharply when the excitation amplitude reaches a certain threshold. In this paper, through establishing the electrical-mechanical coupling numerical model for a piezoelectric metastructure with bistable-circuit shunts, we investigate its nonlinear vibration transmission properties. It is found that, in the local-resonance bandgap of the linearized metastructure around stable equilibria, the supratransmission thresholds exhibit distinctions when the excitation amplitude sweeps up versus down, indicating the emergence of a hysteresis effect in supratransmission. The supratransmission hysteresis range can be effectively shifted through adjusting the distance between the two stable equilibria or weakening the resonance intensity of circuits around them. Furthermore, it is observed that by configurating linear resonant circuits on one side of the metastructure to introduce a system asymmetry, the supratransmission hysteresis ranges of the forward and backward directions deviate away from each other. This nonreciprocal hysteresis effect can enable appearance of different patterns of nonreciprocal codes with respect to the excitation amplitude ranges. The deviation of the supratransmission hysteresis range can be improved if a larger system asymmetry is used, making this sort of nonreciprocal code adaptive. Overall, this research extends the nonreciprocity property of metamaterials, which is not limited to the settled “transmission” or “non-transmission” states of conventional metamaterials in the two opposite directions. It opens up possibilities for achieving unidirectional transmission of elastic information.