The emerging Graph Convolutional Networks (GCNs) have attracted widespread attention in graph learning, due to their good ability of aggregating the information between higher-order neighbors. However, real-world graph data contains high noise and redundancy, making it hard for GCNs to accurately depict the complete relationships between nodes, which seriously degrades the quality of graph representations. Moreover, existing studies commonly ignore the distribution difference between feature and semantic spaces in graphs, causing inferior model generalization. To address these challenges, we propose DIB-RGCN, a novel robust GCN framework, to explore the optimal graph representation with the guidance of the well-designed dual information bottleneck principle. First, we analyze the reasons for distribution differences and theoretically prove that minimal sufficient representations in specific spaces cannot promise optimal performance for downstream tasks. Next, we design new dual channels to regularize feature and semantic spaces, eliminating the sharing of task-irrelevant information between spaces. Different from existing denoising algorithms that adopt a random dropping manner, we innovatively replace potential noisy features and edges with local neighboring representations. This design lowers edge-specific coefficient assignment, alleviating the interference of original representations while retaining graph structures. Further, we maximize the sharing of task-relevant information between feature and semantic spaces to alleviate the difference between them. Using real-world datasets, extensive experiments demonstrate the robustness of the proposed DIB-RGCN, which outperforms state-of-the-art methods on classification tasks.