Compressive sensing (CS), as a new sensing/sampling paradigm, facilitates signal acquisition by reducing the number of samples required for reconstruction of the original signal, and thus appears to be a promising technique for applications where the sampling cost is high, e.g., the Nyquist rate exceeds the current capabilities of analog-to-digital converters (ADCs). Conventional CS, although effective for dealing with one signal, only leverages the intra-signal correlation for reconstruction. This paper develops a decentralized Bayesian reconstruction algorithm for networked sensing systems to jointly reconstruct multiple signals based on the distributed compressive sensing (DCS) model that exploits both intra- and inter-signal correlations. The proposed approach is able to address networked sensing system applications with privacy concerns and/or for a fusion-centre-free scenario, where centralized approaches fail. Simulation results demonstrate that the proposed decentralized approaches have good recovery performance and converge reasonably quickly