Current shadow-object instance detection methods rely on fully supervised training with mask labels. However, mask labeling is both complex and costly. Utilizing only bounding box labels for training can reduce annotation challenges and costs, but this weak supervision may decrease the accuracy of instance mask predictions. To address this issue, weakly supervised methods were first utilized for shadow-object instance detection. A weakly supervised shadow-object instance detection approach with bidirectional learning network is proposed. Firstly, a teacher-student bidirectional learning structure was designed, utilizing the predicted results of the teacher network as pseudo mask labels for the supervised training of the student network. The accuracy of weakly supervised detection was enhanced by updating the parameters of the teacher network using the exponential moving average method. Secondly, the prediction mask is precisely positioned using projection loss, and a color affinity index is introduced to represent the color prior information of the image. By integrating this with the cross-entropy loss function, a color affinity loss function is designed to enhance the network's overall detection performance. To verify the effectiveness of the proposed method and enhance the network's robustness, a shadow-object instance detection dataset was constructed. The predictive capability of the network was validated using both this dataset and the public dataset SOBA, with average precision values of 53.3 and 51.5, respectively.