Current approaches to testing and debugging NLP models rely on highly variable human creativity and extensive labor, or only work for a very restrictive class of bugs. We present AdaTest, a process which uses large scale language models (LMs) in partnership with human feedback to automatically write unit tests highlighting bugs in a target model. Such bugs are then addressed through an iterative text-fix-retest loop, inspired by traditional software development. In experiments with expert and non-expert users and commercial / research models for 8 different tasks, AdaTest makes users 5-10x more effective at finding bugs than current approaches, and helps users effectively fix bugs without adding new bugs.