A machine learning approach to damage detection is presented for a bridge structural health monitoring (SHM) system. The method is validated on the renowned Z24 bridge benchmark dataset where a sensor instrumented, three-span bridge was monitored for almost a year before being deliberately damaged in a realistic and controlled way. Several damage cases were successfully detected, making this a viable approach in a data-based bridge SHM system. The method addresses directly a critical issue in most data-based SHM systems, which is that the collected training data will not contain all natural weather events and load conditions. A SHM system that is trained on such limited data must be able to handle uncertainty in its predictions to prevent false damage detections. A Bayesian autoencoder neural network is trained to reconstruct raw sensor data sequences, with uncertainty bounds in prediction. The uncertainty-adjusted reconstruction error of an unseen sequence is compared to a healthy-state error distribution, and the sequence is accepted or rejected based on the fidelity of the reconstruction. If the proportion of rejected sequences goes over a predetermined threshold, the bridge is determined to be in a damaged state. This is a fully operational, machine learning-based bridge damage detection system that is learned directly from raw sensor data.