We present a Bayesian nonparametric regression method for zero-inflated outcomes. This work is motivated by a need for estimates of causal treatment effects on medical costs; that is, estimates contrasting average total costs that would have accumulated under one treatment versus another. However, cost data tend to be heavily zero-inflated, skewed, and multi-modal. This presents a significant statistical challenge, even if the usual causal identification assumptions are satisfied. Our method flexibly models expected cost conditional on treatment and covariates. This mean model is incorporated into the g-formula to obtain nonparametric estimates of causal effects. Moreover, the estimation procedure predicts latent cluster membership for each patient - automatically identifying groups of patients who have similar cost-covariate associations. We present a generative model, an MCMC method for sampling from the posterior, and simulation results assessing regression performance under various settings. Lastly, we apply the method to costs in the SEER Medicare database.