The bridge structure is subjected to environmental erosion and increasing correlated load impacts during its service life. These factors cause bridge resistance deterioration and make its safety performance less optimistic. To accurately evaluate bridge safety performance in its remaining service life, it is essential to consider the non-stationary characteristics of structural resistance degradation and the time correlativity of load effects. Under the framework of time-dependent reliability, a reliability equation based on Bayesian theory is proposed by using Gamma distribution to describe the non-stationary degradation of bridge resistance while adopting two-dimensional joint distribution function of adjacent loads to express their time correlativity. Monte Carlo simulation is then used to verify the results. The analysis to a simply supported RC bridge in Sichuan province shows that: the results of the equation are close to numerical solutions of MCS when the double integral of molecule of a single conditional probability is greater than 0.7, which proves its correctness; the larger scale parameter of Gamma degradation process and the weaker time-correlativity of load effects will lead to greater structural time-dependent failure probability; when the annual growth rate of vehicle load intensity is higher than 2%, the bridge failure probability within 30 years is relatively large, where regular inspection, maintenance and repair are required.