Facing the challenges on the accurate and effective prediction under extreme loads, machine learning has gradually demonstrated its potential to replace traditional methods. Existing approaches primarily focus on predicting the peak overpressure or impulse of explosive shock waves, with limited research on predicting the reflected overpressure time history. Load-time history prediction encompasses not only the peak overpressure but also embraces various multi-dimensional information including duration, waveform, and impulse, thereby offering a more comprehensive depiction of the dynamic temporal and spatial characteristics of shock waves. To address this issue, a prediction model for bridge surface reflected overpressure time history is proposed, targeting a planar shock wave diffracting around a bridge section. This model is based on principal component analysis (PCA) and back propagation neural network (BPNN) algorithm with multi-task learning. A loss function considering the impact of peak overpressure and maximum impulse is introduced to fully consider the potential correlations between different modes after PCA dimension reduction. This enables the model to effectively predict bridge shock wave load time histories under varying incident overpressure. Through the analysis of three types of BPNN models, multi-task learning model, multi-input single-output model, and multi-input multi-output model. It was found that the multitask learning model has the highest prediction accuracy, while the multi-input multi-output model struggles to effectively adapt to the current predictive task requirements. The multitask learning model, used for predicting, achieves high precision in forecasting the time history of reflected overpressure at various measurement points on the bridge surface and the peak overpressure values, with R² values of 0.792 and 0.987. It also closely matches the simulation values in predicting the time history of combined forces and torque acting on the box girder. Additionally, this model performs better in interpolative value prediction than in extrapolative value prediction, but it also demonstrates a certain capability in predicting extrapolative values.