The ability to dynamically process mechanical signals is crucial for advanced functionalities in soft robotics and mechanosensing, where classical viscoelastic materials often lack intrinsic tunabil- ity and quantitative design rules are missing. In this work, we show that incorporating internal bistability provides a simple but powerful mechanism to tailor response and signal attenuation in mechanical (meta)materials. In our model, the bistable elements switch discretely with a predefined intrinsic timescale between states distinguished by a change in potential energy ϵ, equilibrium length ∆l, and spring constant ∆k. The model is simulated numerically by microscopic Brownian dynamics coupled to discrete Poisson switching with rate ν. In addition we develop a nonlinear continuum (field) theory that describes the macroscopic strain relaxation. Crucially, the model yields closed- form analytical solutions for the linear response and the spatial penetration depth, revealing two complementary phenomena: a universal screening mechanism (akin to the electrostatic ‘skin effect’) that strongly reduces spatial signal penetration when the driving frequency exceeds the internal relaxation rate, and a frequency-insensitive response plateau emerging from timescale separation. The attenuation strength, expressed by a screening length, is controlled primarily by the conforma- tional length change ∆l, while both the attenuation regime and plateau position are tuneable via the switching rate ν. A systematic parameter study exposes a fundamental design trade-off: while larger conformational changes ∆l strengthen dissipation, they simultaneously raise the (elastic) en- ergy barrier for state transitions, eventually triggering state-locking where the damping vanishes. Optimal signal attenuation thus emerges from a compromise between pronounced bistability and a surmountable barrier. Due to its analytical tractability and generic formulation, our framework provides explicit design rules for fine-tuning the adaptive response of mechanical bistable media. It is readily applicable to a wide range of experimental bistable systems – from biopolymers to synthetic catch bonds and metamaterials – providing a quantitative foundation for the predictive design of soft materials with frequency-selective mechanical response.