Microseismic signal denoising is a crucial step in microseismic monitoring because it directly affects the reliability of subsequent processing and interpretation. To address the low amplitude feature of microseismic signals, the complexity and nonstationarity of background noise, and the limitations of existing data-driven and physics-guided methods, this study proposes RC-BiLSTM, a lightweight two-stage denoising framework based on a dynamical-system consistency prior. Rather than imposing an explicit physics-constrained residual, the proposed framework uses a soft dynamical prior to represent noisy microseismic records as the superposition of a temporally coherent dominant component and stochastic perturbations. In the first stage, reservoir computing (RC) performs coarse denoising by representing the dominant dynamical features of the waveform in a high-dimensional recurrent state. In the second stage, the RC estimate and the explicit residual are fed into a bidirectional long short-term memory network (BiLSTM), which learns a residual refinement to recover weak waveform details and suppress complex nonstationary noise. Numerical experiments on both synthetic and field data demonstrate that RC-BiLSTM achieves effective denoising performance under the tested conditions and exhibits improved stability under medium-parameter perturbations. Field-data tests further suggest its potential for improving microseismic waveform quality in practical monitoring scenarios.