The present study provides a Bayesian framework for the estimation of the yaw angle and the pressure distribution on the surface of the vehicle from the spatially sparse pressure measurements obtained by optimized sensing locations and data-driven models. The framework is demonstrated on the Ahmed model which is the simplified car model. The yaw angle and the pressure distribution on the top surface of the Ahmed model are estimated based on the sparse pressure measurement on the top surface. The estimation models are constructed based on the time-averaged pressure distribution on the top surface of the car model with various yaw angles obtained by a pressure-sensitive paint technique. The estimation model for the yaw angle was constructed as the linear regression between the yaw angle and pressure at the sensing locations, and the estimation model for the pressure distribution was constructed from a POD-based reduced order model. The Bayesian estimation was newly adopted for the mode coefficient estimation of the reduced-order model of the pressure distribution, and the optimization method of the sensing locations for the Bayesian estimation was adopted. The performance of the present Bayesian method was compared with previously proposed methods, and the results showed that the Bayesian method provides the best performance under most conditions on the yaw angle estimation and the pressure distribution reconstruction. In addition, various combinations of the estimation method and sensing location optimization method were tested, and the impact of estimation and sensing locations was discussed.