In Structural Health Monitoring (SHM), maintaining infrastructure integrity under seismic conditions presents significant challenges, particularly due to uncertainties in the structural properties required for accurate numerical modeling. To address these challenges, this study proposes a Bayesian Neural Network (BNN) framework designed to detect and quantify seismically induced damaged states in structures over time. By integrating multi-source data from various monitoring sensors, the BNN leverages recent advancements in artificial intelligence to provide probabilistic predictions. Unlike traditional neural networks, the BNN is particularly effective when working with limited datasets and excels at updating predictions as new information becomes available. In this work, a prestressed concrete box-girder bridge with vertically prestressed internal joints is used as a representative case. A Finite Element Model (FEM) of the bridge is developed and calibrated using data from Ambient Vibration Tests. The SHM system comprises a sensor network distributed along the girder and substructure, enabling monitoring of both dynamic characteristics and static responses under simulated seismic damage scenarios. The BNN is trained on such sensory data to infer local variations in structural stiffness, especially targeting the substructure, to solve the inverse problem of seismic damage detection, localization, and quantification. Parametric analyses show that the BNN can effectively detect likely damage patterns resulting from seismic events, providing confidence intervals for each prediction. Importantly, the Bayesian learning process allows for continuous model refinement as new seismic or post-event inspection data are collected, enhancing the long-term robustness and reliability of SHM-based decision-making in seismically prone regions.