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The prospect of a system possessing two or more stable states for a given excitation condition is of topical interest with applications in information processing networks. In this work, we establish the remote transfer of bistability from a nonlinear resource in a dissipatively coupled two-mode system. As a clear advantage over coherently coupled settings, the dissipative nature of interaction is found to support a lower pumping threshold for bistable signals. For comparable parameters, the bistability threshold for dissipatively coupled systems is lower by a factor of about 5. The resulting hysteresis can be studied spectroscopically by applying a probe field through the waveguide and examining the polariton character of the transmitted field. Our model is generic, apropos of an extensive set of quantum systems, and we demonstrate our results in the context of magnonics where experimental interest has flourished of late …