To predict the bridge coupled extreme stress more reasonably，the bridge monitoring extreme stresses are regarded as the multi-component signals coupled with multi-modal responses. Based on the advantages of Hilbert signal decomposition and Hilbert square demodulation（HSD）technology in terms of the demodulation of multi-component signals，the Bayesian Hilbert Dynamic Linear Model（BHDLM）is proposed for the dynamic prediction of bridge extreme stress. The monitoring extreme stresses are decoupled into several mono-component extreme stresses by the Hilbert signal decomposition technique. The Hilbert Dynamic Linear Model（HDLM）of each mono-component extreme stress is developed by the HSD subsequently. Based on the mono-component extreme stress and the Bayesian method，the probability recursive processes of HDLM are introduced to dynamically predict the mono-component extreme stresses. Once the dynamic prediction of the mono-component extreme stresses is realized，the bridge coupled extreme stress data can be further obtained successfully. The validity of the proposed model is verified by the monitoring data of a bridge in service. The results show that the proposed HDLM based on the decoupled mono-component extreme stress can take account of the periodicity，randomness of the monitoring data despite the simple process of HDLM，and can be used to dynamically predict the bridge extreme stresses with Bayesian method.