Recent years have witnessed significant advances in image deraining tasks due to the emergence of numerous effective Transformers and multi-layer perceptron (MLP) models. However, these models still rely on unidirectional information flow and fail to fully exploit the potentially useful information from multiple image scales, thus limiting the robustness of the models in complex rainy scenes. To this end, we develop an effective closed-loop bidirectional scale-recurrent network (called CBS-Net) for image deraining, which organically integrates both Transformer and MLP models to jointly explore multi-scale rain representations. Specifically, we introduce a sparse Transformer block within the intra-scale branch to adaptively capture the most useful content-aware features. Furthermore, we construct a dimensional MLP block within the inter-scale branch to dynamically modulate spatial-aware features from different scales. To ensure more accurate bidirectional estimations in our scale-recurrent network, a simple yet effective feedback propagation block is embedded to perform coarse-to-fine and fine-to-coarse information communication. Extensive experimental results show that our approach achieves state-of-the-art performance on multiple benchmark datasets, demonstrating its effectiveness and scalability.