Accurate state estimation is fundamental to intelligent vehicles. Wheel load, one of the most important chassis states, serves as an essential input for advanced driver assistance systems (ADAS) and exerts a direct influence on vehicle stability and safety. However, wheel load estimation remains challenging due to the complexity of chassis modeling and the susceptibility of nonlinear systems to noise. To address these issues, this paper first introduces a refined suspension linkage-level modeling approach that constructs a nonlinear instantaneous dynamic model by explicitly considering the complex geometric structure of the suspension. Building upon this, we propose a damper characteristics-based Bayesian physics-informed neural network (Damper-B-PINN) framework to estimate dynamic wheel load, which leverages the suspension dynamics as physical guidance of PINN while employing Bayesian inference to mitigate the effects of system noise and uncertainty. Moreover, a damper-characteristic physics conditioning (DPC) module is designed for embedding physical prior. The proposed Damper-B-PINN is evaluated using both high-fidelity simulation datasets generated by CarSim software and real-world datasets collected from a Formula Student race car. Experimental results demonstrate that our Damper-B-PINN consistently outperforms existing methods across various test conditions, particularly extreme ones. These findings highlight the potential of the proposed Damper-B-PINN framework to enhance the accuracy and robustness of dynamic wheel load estimation, thereby improving the reliability and safety of ADAS applications.