Characterizing brain dynamic functional connectivity (dFC) patterns from functional Magnetic Resonance Imaging (fMRI) data is of paramount importance in neuroscience and medicine. Recently, many graph neural network (GNN) models, combined with transformers or recurrent neural networks (RNNs), have shown great potential for modeling the dFC patterns. However, these methods face challenges in effectively characterizing the modularity organization of brain networks and capturing varying dFC state patterns. To address these limitations, we propose dFCExpert, a novel method designed to learn robust representations of dFC patterns in fMRI data with modularity experts and state experts. Specifically, the modularity experts optimize multiple experts to characterize the brain modularity organization during graph feature learning process by combining GNN and mixture of experts (MoE), with each expert focusing on brain nodes within the same functional network module. The state experts aggregate temporal dFC features into a set of distinctive connectivity states using a soft prototype clustering method, providing insight into how these states support different brain activities or are differentially affected by brain disorders. Experiments on two large-scale fMRI datasets demonstrate the superiority of our method over existing alternatives. The learned dFC representations not only show improved interpretability but also hold promise for enhancing clinical diagnosis.