The liver can substantially regenerate after injury, with both main epithelial cell types, hepatocytes and biliary epithelial cells (BECs), playing important roles in parenchymal regeneration. Beyond metabolic functions, BECs exhibit substantial plasticity and in some contexts can drive hepatic repopulation. Here, we performed single-cell RNA sequencing to examine BEC and hepatocyte heterogeneity during homeostasis and after injury. Instead of evidence for a transcriptionally defined progenitor-like BEC cell, we found significant homeostatic BEC heterogeneity that reflects fluctuating activation of a YAP-dependent program. This transcriptional signature defines a dynamic cellular state during homeostasis and is highly responsive to injury. YAP signaling is induced by physiological bile acids (BAs), required for BEC survival in response to BA exposure, and is necessary for hepatocyte reprogramming into biliary progenitors upon injury. Together, these findings uncover molecular heterogeneity within the ductal epithelium and reveal YAP as a protective rheostat and regenerative regulator in the mammalian liver.