Bimanual dexterous manipulation is a critical yet underexplored area in robotics. Its high-dimensional action space and inherent task complexity present significant challenges for policy learning, and the limited task diversity in existing benchmarks hinders general-purpose skill development. Existing approaches largely depend on reinforcement learning, often constrained by intricately designed reward functions tailored to a narrow set of tasks. In this work, we present a novel approach for efficiently learning diverse bimanual dexterous skills from abundant human demonstrations. Specifically, we introduce BiDexHD, a framework that unifies task construction from existing bimanual datasets and employs teacher-student policy learning to address all tasks. The teacher learns state-based policies using a general two-stage reward function across tasks with shared behaviors, while the student distills the learned multi-task policies into a vision-based policy. With BiDexHD, scalable learning of numerous bimanual dexterous skills from auto-constructed tasks becomes feasible, offering promising advances toward universal bimanual dexterous manipulation. Experiments on TACO tool-using dataset spanning 141 tasks across 6 categories demonstrate a task fulfillment rate of 74.59% on trained tasks and 51.07% on unseen tasks. We further transfer BiDexHD to 11 ARCTIC collaborative tasks and achieve an average of 80.49% task fulfillment rate on trained tasks and 65.99% on unseen task. All empirical results demonstrate the effectiveness and competitive zero-shot generalization capabilities of BiDexHD.