3D conducting motion generation aims to synthesize fine-grained conductor motions from music, with broad potential in music education, virtual performance, digital human animation, and human-AI co-creation. However, this task remains underexplored due to two major challenges: (1) the lack of large-scale fine-grained 3D conducting datasets and (2) the absence of effective methods that can jointly support long-sequence generation with high quality and efficiency. To address the data limitation, we develop a quality-oriented 3D conducting motion collection pipeline and construct CM-Data, a fine-grained SMPL-X dataset with about 10 hours of conducting motion data. To the best of our knowledge, CM-Data is the first and largest public dataset for 3D conducting motion generation. To address the methodological limitation, we propose BiTDiff, a novel framework for 3D conducting motion generation, built upon a BiMamba-Transformer hybrid model architecture for efficient long-sequence modeling and a Diffusion-based generative strategy with human-kinematic decomposition for high-quality motion synthesis. Specifically, BiTDiff introduces auxiliary physical-consistency losses and a hand-/body-specific forward-kinematics design for better fine-grained motion modeling, while leveraging BiMamba for memory-efficient long-sequence temporal modeling and Transformer for cross-modal semantic alignment. In addition, BiTDiff supports training-free joint-level motion editing, enabling downstream human-AI interaction design. Extensive quantitative and qualitative experiments demonstrate that BiTDiff achieves state-of-the-art (SOTA) performance for 3D conducting motion generation on the CM-Data dataset. Code will be available upon acceptance.