Typical Bayesian approaches to OOD detection use epistemic uncertainty. Surprisingly from the Bayesian perspective, there are a number of methods that successfully use aleatoric uncertainty to detect OOD points (e.g. Hendryks et al. 2018). In addition, it is difficult to use outlier exposure to improve a Bayesian OOD detection model, as it is not clear whether it is possible or desirable to increase posterior (epistemic) uncertainty at outlier points. We show that a generative model of data curation provides a principled account of aleatoric uncertainty for OOD detection. In particular, aleatoric uncertainty signals a specific type of OOD point: one without a well-defined class-label, and our model of data curation gives a likelihood for these points, giving us a mechanism for conditioning on outlier points and thus performing principled Bayesian outlier exposure. Our principled Bayesian approach, combining aleatoric and epistemic uncertainty with outlier exposure performs better than methods using aleatoric or epistemic alone.