Disease progression models, in which a patient's latent severity is modeled as progressing over time and producing observed symptoms, have developed great potential to help with disease detection, prediction, and drug development. However, a significant limitation of existing models is that they do not typically account for healthcare disparities that can bias the observed data. We draw attention to three key disparities: certain patient populations may (1) start receiving care only when their disease is more severe, (2) experience faster disease progression even while receiving care, or (3) receive care less frequently conditional on disease severity. To address this, we develop an interpretable Bayesian disease progression model that captures these three disparities. We show theoretically and empirically that our model correctly estimates disparities and severity from observed data, and that failing to account for these disparities produces biased estimates of severity.