A robust model-free adaptive iterative learning control (R-MFAILC) algorithm is proposed in this work to address the issue of laterally controlling an autonomous bus. First, according to the periodic repetitive working characteristics of autonomous buses, a novel dynamic linearized method used in the iterative domain is utilized, and a time-varying data model with a pseudo gradient (PG) is given. Then, the R-MFAILC controller is designed with a proposed adaptive attenuation factor. The proposed algorithm's advantage lies in the R-MFAILC controller, which solely utilizes the input and output data of the regulated entity. Moreover, the R-MFAILC controller has strong robustness and can handle the nonlinear measurement disturbances of the system. In simulations based on the Truck-Sim simulation platform, the effectiveness of the proposed algorithm is verified. A rigorous mathematical analysis is employed to demonstrate the stability and convergence of the proposed algorithm.