Wheeled bipedal robots (WBRs) have the capability to execute agile and versatile locomotion tasks. This paper focuses on improving the dynamic performance of WBRs through innovations in both hardware and software development. Inspired by the human barbell squat, a bionic mechanical design is proposed and implemented as shown in Fig. 1. It distributes the weight onto its hip and knee joints to improve the effectiveness of joint motors while maintaining a relatively large workspace of the base link. Meanwhile, a novel model-based controller is devised, synthesizing height-variable wheeled linear inverted pendulum (HV-wLIP) model, Control Lyapunov Function (CLF) and whole-body dynamics for theoretically guaranteed stability and efficient computation. Compared with other alternatives, as a more accurate approximation of the WBR dynamics, the HV-wLIP can enable more agile response and provide theory basis for WBR controller design. Experimental results demonstrate that the robot could perform human-like deep squat, and is capable of maintaining tracking CoM velocity while manipulating base states. Furthermore, it exhibited robustness against external disturbances and unknown terrains even in the wild.