Operational modal analysis is inevitably affected by multiple uncertainties such as measurement noise, modeling error, etc. The Bayesian operational modal analysis is a promising candidate for ambient modal analysis since it presents a rigorous way for deriving the optimal modal properties and their associated uncertainties. It has been revealed that the interaction between spectrum variables (e.g., frequency, damping ratio as well as the magnitude of modal excitation and prediction error) and spatial variables (e.g., mode shape components) can be decoupled completely by analyzing the statistics of auto-power spectral density and cross-power spectral density. Based on the variable separation technique, a two-stage fast Bayesian spectral density approach (BSDA) could be proposed for operational modal analysis. In this study, the efficiency and accuracy of the methodology are verified by using the ambient vibration testing data of Bei-chuan River steel arch bridge located in China. The spectrum variables and their associated uncertainties can be identified in the first stage, based on the statistical properties of the trace of a spectral density matrix, while the spatial variables and their uncertainties can be extracted instantaneously in the second stage by using the statistical properties of a power spectral density matrix. The analysis results are compared with different classic approaches. Comparison results indicate that the proposed method can achieve satisfactory results and it can resolve the difficulties of computational inefficiency and ill-conditioning of conventional BSDA. Finally, the effects of bandwidth on the identification results are investigated in detail. Investigation results indicate that the uncertainty of prediction errors are more vulnerable to the frequency band.