This paper develops a performant Bayesian approach to conditional average treatment effect (CATE) estimation in regression discontinuity designs (RDD), an increasingly prevalent form of quasi-experiment that facilitates causal inference. Earlier Bayesian approaches do not easily accommodate CATE estimation while recent frequentist approaches to this problem assume a known basis expansion, a steep model specification requirement that our approach avoids. The new model is a variant of a Bayesian additive regression tree (BART) model with linear leaf-level regressions on the running variable and a treatment dummy (and their interaction). The model adaptively partitions covariate space into regions where the slope on the running variable appreciably differs, providing interpretable Bayesian inference on conditional average treatment effects near the cutoff.