Assembly is a fundamental skill for robots in both modern manufacturing and service robotics. Existing datasets aim to address the data bottleneck in training general-purpose robot models, falling short of capturing contact-rich assembly tasks. To bridge this gap, we introduce SharedAssembly, a novel bilateral teleoperation approach with shared autonomy for scalable assembly execution and data collection. User studies demonstrate that the proposed approach enhances both success rates and efficiency, achieving a 97.0% success rate across various sub-millimeter-level assembly tasks. Notably, novice and intermediate users achieve performance comparable to experts using baseline teleoperation methods, significantly enhancing large-scale data collection.