Traditional Chinese Bone-setting (TCB) involves complex movements and force feedback, which are critical for effective fracture reduction. However, its practice necessitates the collaboration of highly experienced surgeons, and the availability of expert resources is significantly limited. These challenges have significantly hindered the inheritance and dissemination of TCB techniques. The advancement of Learning from Demonstration offers a promising solution for addressing this challenge. In this study, we developed an innovative framework of closed reduction skill learning and dual-layer hybrid admittance control for a dual-arm bone-setting robot, specifically targeting ankle fracture. The framework began with a comprehensive structural design of the robot, incorporating analyses of closed-chain kinematics and the decomposition of internal and external forces. Additionally, we introduced a globally optimal reparameterization algorithm for temporal alignment of demonstrations and extended the Motion/Force Synchronous Kernelized Movement Primitive to learn reduction maneuvers and forces. Furthermore, we designed a dual-layer hybrid admittance controller, consisting of an ankle-layer and a robot- layer. Specifically, we propose a novel adaptive fuzzy variable admittance control strategy for the ankle-layer to achieve accurate tracking of reduction forces, which reduces the RMSE of force tracking along the X-axis by 50.35% compared to the non-fuzzy strategy. The experimental results demonstrated that the framework successfully replicates the human-like bone-setting process and can imitate personalized bone-setting trajectories under expert guidance.