InferenceQL is a probabilistic programming system for scalable Bayesian AutoML from database tables. InferenceQL is designed to help make Bayesian approaches to data analysis more accessible to broad audiences and to assist experts in auditing and improving the quality of data, models, and inferences. Unlike traditional probabilistic programming systems, InferenceQL provides automation for learning models online using nonparametric Bayesian structure learning of probabilistic programs. Experts can override these models with custom probabilistic programs for specific subsets of variables and conditional distributions. For a broad class of models, InferenceQL can generate realistic synthetic data subject to constraints and can automatically compute exact probabilities and mutual information values. Finally, InferenceQL aims to enable scalable Bayesian model criticism via posterior predictive checks, data quality screening via conditional probability calculation, fairness auditing via conditional probability ratios, and synthetic data generation to enhance privacy. These capabilities are accomplished using constructs that interleave standard database queries with Bayesian inference.