Proteins often undergo structural perturbations upon binding to other proteins or ligands or when they are subjected to environmental changes. Hydrogen−deuterium exchange mass spectrometry (HDX-MS) can be used to explore conformational changes in proteins by examining differences in the rate of deuterium incorporation in different contexts. To determine deuterium incorporation rates, HDX-MS measurements are typically made over a time course. Recently introduced methods show that incorporating the temporal dimension into the statistical analysis improves power and interpretation. However, these approaches have technical assumptions that hinder their flexibility. Here, we propose a more flexible methodology by reframing these methods in a Bayesian framework. Our proposed framework has improved algorithmic stability, allows us to perform uncertainty quantification, and can calculate statistical quantities that are inaccessible to other approaches. We demonstrate the general applicability of the method by showing it can perform rigorous model selection on a spike-in HDX-MS experiment, improved interpretation in an epitope mapping experiment, and increased sensitivity in a small molecule case-study. Bayesian analysis of an HDX experiment with an antibody dimer bound to an E3 ubiquitin ligase identifies at least two interaction interfaces where previous methods obtained confounding results due to the complexities of conformational changes on binding. Our findings are consistent with the cocrystal structure of these proteins, demonstrating a bayesian approach can identify important binding epitopes from HDX data. We also generate HDX-MS data of the bromodomain-containing protein BRD4 in complex with GSK1210151A to demonstrate the increased sensitivity of adopting a Bayesian approach.