As electronic systems become increasingly complex and prevalent in modern vehicles, securing onboard networks is crucial, particularly as many of these systems are safety-critical. Researchers have demonstrated that modern vehicles are susceptible to various types of attacks, enabling attackers to gain control and compromise safety-critical electronic systems. Consequently, several Intrusion Detection Systems (IDSs) have been proposed in the literature to detect such cyber-attacks on vehicles. This paper introduces a novel generative classifier-based Intrusion Detection System (IDS) designed for anomaly detection in automotive networks, specifically focusing on the Controller Area Network (CAN). Leveraging variational Bayes, our proposed IDS utilizes a deep latent variable model to construct a causal graph for conditional probabilities. An auto-encoder architecture is utilized to build the classifier to estimate conditional probabilities, which contribute to the final prediction probabilities through Bayesian inference. Comparative evaluations against state-of-the-art IDSs on a public Car-hacking dataset highlight our proposed classifier's superior performance in improving detection accuracy and F1-score. The proposed IDS demonstrates its efficacy by outperforming existing models with limited training data, providing enhanced security assurance for automotive systems.