Teleoperation is a crucial tool for collecting human demonstrations, but controlling robots with bimanual dexterous hands remains a challenge. Existing teleoperation systems struggle to handle the complexity of coordinating two hands for intricate manipulations. We introduce Bunny-VisionPro, a real-time bimanual dexterous teleoperation system that leverages a VR headset. Unlike previous vision-based teleoperation systems, we design novel low-cost devices to provide haptic feedback to the operator, enhancing immersion. Our system prioritizes safety by incorporating collision and singularity avoidance while maintaining real-time performance through innovative designs. Bunny-VisionPro outperforms prior systems on a standard task suite, achieving higher success rates and reduced task completion times. Moreover, the high-quality teleoperation demonstrations improve downstream imitation learning performance, leading to better generalizability. Notably, Bunny-VisionPro enables imitation learning with challenging multi-stage, long-horizon dexterous manipulation tasks, which have rarely been addressed in previous work. Our system's ability to handle bimanual manipulations while prioritizing safety and real-time performance makes it a powerful tool for advancing dexterous manipulation and imitation learning.