Reconfigurable intelligent surface (RIS)-aided vehicle-to-everything (V2X) communication has emerged as a crucial solution for providing reliable data services to vehicles on the road. However, in delay-sensitive or high-mobility communications, the rapid movement of vehicles can lead to random scattering in the environment and time-selective fading in the channel. In view of this, we investigate in this paper an innovative linear model with low-complexity transmitter signal design and receiver detection methods, which boost stability in fast-fading environments and reduce channel training overhead. Specifically, considering the differences in hardware design and signal processing at the receiving end between uplink and downlink communication systems, distinct solutions are proposed. Accordingly, we first integrate the Rician channel introduced by the RIS with the corresponding signal processing algorithms to model the RIS-aided downlink communication system as a Doppler-robust linear model. Inspired by this property, we design a precoding scheme based on the linear model to reduce the complexity of precoding. Then, by leveraging the linear model and the large-scale antenna array at the base station (BS) side, we improve the linear model for the uplink communication system and derive its asymptotic performance in closed-form. Simulation results demonstrate the performance advantages of the proposed RIS-aided high-mobility communication system compared to other benchmark schemes.