Traditional regression models covariates on the mean value of the response variable, while quantile regression (QR) allows one to study the effect of covariates across the entire response distribution. However, QR methods have been primarily applied to continuous response variables from a single data-generating process, and the few studies that have performed QR on count data have not accounted for excess zeros from a Bayesian perspective. This being the case, we propose a Bayesian two-part QR model for count data with excess zeros, and we compare the proposed model to a frequentist approach via simulation. Furthermore, two applications are presented to display the model's usefulness on real data, with differing effects across the response distribution identified for multiple covariates in both cases. The nature of those effects in the outermost quantiles of the response distribution is given particular attention.