Bridge bearings play significant roles in the mechanical responses of bridges and foundations and impact the operation of bridges. This paper presents an adaptive bearing with adjustable height and develops an approach to control bearings toward smart bridges based on Physics-Informed Neural Network (PINN). The approach integrates the mechanical governing equation, which describes the relationship between bridge responses and bearing heights, with data-driven neural networks, enabling efficient prediction of bearing reaction forces and effective optimization of bearing heights for controlling the reaction forces. The effectiveness of the approach is evaluated by examining various types of bridges. The results showed that the proposed approach outperformed 20 machine learning models. The case study showed that the approach effectively limited the force adjustment error to 18 % while reducing both vehicle-bridge response and displacement on bearing top plate. This research will enhance bridge controllability, thereby improving bridge operation.