This study proposes a numerical investigation for rapid bridge damage detection based on a semi-supervised deep learning (DL) model and a damage index (DI)-based Gaussian process. The proposed damage detection method uses bridge response data (acceleration and displacement data) from various damage scenarios within a simply supported girder bridge subjected to a two-axle moving vehicle load. As for semi-supervised learning, we used a one-class convolutional neural network (OC-CNN) model. This model combines a one-class (OC) classification algorithm with a simple one-dimensional convolutional neural network (1D CNN) configuration. The performance of the proposed OC-CNN model was evaluated through a numerical example of a vehicle-bridge coupling system. The proposed OC-CNN model trained using acceleration data showed promising results for different vehicle weights and speeds. These results offer confidence in using the prediction error loss of the proposed OC-CNN model as an ideal damage-sensitive feature for rapid bridge damage detection. In addition, the Gaussian process used in the DI can classify the prediction error losses resulting from the change induced by different damage severities (10%, 20%, and 30%) and different types of damage scenarios (single damage, double damages, and multiple damages). These results emphasize the potential of the proposed damage detection method to monitor the state of bridges in practical engineering.