This study introduces an innovative approach for predicting stress responses in steel bridges, specifically focusing on a railway bridge in Vänersborg, Sweden. Four deep learning models have been evaluated: Multilayer Perceptron (MLP), Long Short-Term Memory (LSTM), Temporal Convolutional Network (TCN), and a hybrid LSTM-TCN. Training on stress history data from a multiscale Finite Element (FE) model and a validation with real-world data from a bridge monitoring system revealed high prediction accuracy near sensor locations, surpassing an R-squared score of 0.9, comparable to the polynomial local response function method. The comparative analysis provides critical insights into the great potential of deep learning-based sequence models for identifying intricate, temporally dependent stress patterns across the bridge, including predictions at points distant from direct sensor measurements. These models demonstrate a notable capability for capturing highly non-linear relationships between stress histories. While sequence models (LSTM, TCN, and hybrid LSTM-TCN) tended to provide conservative estimates impacting fatigue life predictions, the MLP model occasionally underestimated critical stress cycles. This research emphasizes the potential of deep learning techniques for time series to enhance bridge monitoring systems, improve virtual sensing, and enable real-time monitoring capabilities. Our proposed methodology provides a comprehensive understanding of stress data in steel bridges, which is crucial for ensuring their maintenance and safety.