We present UniBiDex a unified teleoperation framework for robotic bimanual dexterous manipulation that supports both VRbased and leaderfollower input modalities UniBiDex enables realtime contactrich dualarm teleoperation by integrating heterogeneous input devices into a shared control stack with consistent kinematic treatment and safety guarantees The framework employs nullspace control to optimize bimanual configurations ensuring smooth collisionfree and singularityaware motion across tasks We validate UniBiDex on a longhorizon kitchentidying task involving five sequential manipulation subtasks demonstrating higher task success rates smoother trajectories and improved robustness compared to strong baselines By releasing all hardware and software components as opensource we aim to lower the barrier to collecting largescale highquality human demonstration datasets and accelerate progress in robot learning.