In this paper, we propose a learned scalable/progressive image compression scheme based on deep neural networks (DNN), named Bidirectional Context Disentanglement Network (BCD-Net). For learning hierarchical representations, we first adopt bit-plane decomposition to decompose the information coarsely before the deep-learning-based transformation. However, the information carried by different bit-planes is not only unequal in entropy but also of different importance for reconstruction. We thus take the hidden features corresponding to different bit-planes as the context and design a network topology with bidirectional flows to disentangle the contextual information for more effective compressed representations. Our proposed scheme enables us to obtain the compressed codes with scalable rates via a one-pass encoding-decoding. Experiment results demonstrate that our proposed model outperforms the state-of-the-art DNN-based scalable image compression methods in both PSNR and MS-SSIM metrics. In addition, our proposed model achieves higher performance in MS-SSIM metric than conventional scalable image codecs. Effectiveness of our technical components is also verified through sufficient ablation experiments.