The performance of reinforced concrete (RC) bridges deteriorates with time under the combined action of environmental effects and loadings. The deterministic degradation models cannot accurately describe the uncertainty and time variability of the degradation process. In this study, the inverse Gaussian process (IGP) and the composite Poisson process were respectively adopted to describe the resistance degradation process and the load effect. The time-dependent reliability analysis method for RC bridge members was established based on the double dual random process model of resistance and load. Furthermore, combined with the monitored data, the Bayesian analysis and the expectation maximization (EM) algorithm were adopted to update the IGP-based resistance deterioration model parameters. Subsequently, a dynamic prediction procedure for the reliability of RC bridge members was proposed. Finally, using the resistance degradation data of a RC T-girder bridge during its 40-year service period, the IGP-based resistance deterioration model parameters were updated at four different service times. The reliability of the proposed dynamic prediction procedure was validated. The research results show that IGP can be used to describe the uncertainty and time variability of the resistance degradation process of RC bridge members. The future reliability level and the remaining service life of RC bridges can be accurately predicted by using the detected resistance degradation data during its service period and the updated IGP-based resistance deterioration model parameters.