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The performance of cooperative vehicular applications is tightly dependent on the reliability of the underneath Vehicle-to-Everything (V2X) communication technology. V2X standards, such as Dedicated Short-Range Communications (DSRC) and Cellular-V2X (C-V2X), which are passing their research phase before being mandated in the US, are supposed to serve as reliable circulatory systems for the time-critical information in vehicular networks; however, they are still heavily suffering from scalability issues in real traffic scenarios. The technology-agnostic notion of Model-Based Communications (MBC) has been proposed in our previous works as a promising paradigm to address the scalability issue and its performance, while acquiring different modeling strategies, has been vastly studied. In this work, the modeling capabilities of a powerful non-parametric Bayesian inference scheme, i.e., Gaussian Processes (GPs), is investigated within the MBC context with more details. Our observations reveal an important potential strength of GP-based MBC scheme, i.e., its capability of accurately modeling different driving behavioral patterns by utilizing only a limited size GP kernel bank. This interesting aspect of integrating GP inference with MBC framework, which has been verified in this work using realistic driving data sets, introduces this architecture as a strong and appealing candidate to address the scalability challenge. The results confirm that our proposed approach over-performs the state of the art research in terms of the required communication rate and GP kernel bank size.