Due to the reduction in bending capacity of RC beams being affected by multiple stochastic uncertainties, employing a deterministic function model to study the bending capacity of RC beams often leads to analysis errors that are difficult to accept. This paper, by analyzing the significant discrepancies between calculated values derived from computational models and results obtained from experiments, adopts a model bias coefficient to describe the uncertainty of the computational model. Building on the consideration of parameter and model uncertainties, this paper establishes a Bayesian neural network model for predicting the bending load capacity of RC beams due to reinforcement corrosion. The model is compared with the traditional Back Propagation (BP) neural networks and the Genetic Algorithm-optimized BP (GA-BP) neural networks. The results indicate that the Bayesian neural network model has the least number of iterations and the highest efficiency, with comparable average prediction accuracy to the commonly used GA-BP neural network model. It improves the accuracy by 7.44% compared to the traditional BP neural network model. Finally, based on case studies, the time-variant probability distribution of the bending carrying capacity of corroded RC beams for a service life of 100 years is obtained. It is concluded that the time-variant probability model of the resistance of corroded RC beams follows a log-normal distribution, and the established Bayesian neural network model for predicting the time-variant resistance of corroded RC beams yields better results.