Mixed effects models are commonly used to analyze longitudinal clustered data. When the data contain excessive zeros, the hurdle mixture model separates zero values and non-zero values and provides a straightforward interpretation. We combine a Bayesian hurdle framework with the Conway-Maxwell-Poisson regression model, which can flexibly account for all levels of dispersion. Extensive simulation studies are conducted to assess the effectiveness of our approach. We also compare the Conway-Maxwell-Poisson model with other models, such as the hurdle Poisson model, the hurdle negative binomial model, and the hurdle quasi-Poisson model. Moreover, we apply our methodology to perform a comprehensive analysis on a longitudinal dental dataset of the Iowa Fluoride Study. The study was designed to investigate the effects of various dietary and non-dietary factors on the progression of dental caries among a cohort of Iowa children at the ages of 5, 9, 13 and 17. The results offer potentially new insights to both statistical practitioners and dental researchers.