When estimating causal effects, unmeasured confounding and model misspecification are both potential sources of bias. We propose a method to simultaneously address both issues in the form of a semi-parametric sensitivity analysis. In particular, our approach incorporates Bayesian Additive Regression Trees into a two-parameter sensitivity analysis strategy that assesses sensitivity of posterior distributions of treatment effects to choices of sensitivity parameters. This results in an easily interpretable framework for testing for the impact of an unmeasured confounder that also limits the number of modeling assumptions. We evaluate our approach in a large-scale simulation setting and with high blood pressure data taken from the Third National Health and Nutrition Examination Survey. The model is implemented as open-source software, integrated into the treatSens package for the R statistical programming language.