A common step in developing an understanding of a vertical domain, e.g. shopping, dining, movies, medicine, etc., is curating a taxonomy of categories specific to the domain. These human created artifacts have been the subject of research in embeddings that attempt to encode aspects of the partial ordering property of taxonomies. We compare Box Embeddings, a natural containment representation of category taxonomies, to partial-order embeddings and a baseline Bayes Net, in the context of representing the Medical Subject Headings (MeSH) taxonomy given a set of 300K PubMed articles with subject labels from MeSH. We deeply explore the experimental properties of training box embeddings, including preparation of the training data, sampling ratios and class balance, initialization strategies, and propose a fix to the original box objective. We then present first results in using these techniques for representing a bipartite learning problem (i.e. collaborative filtering) in the presence of taxonomic relations within each partition, inferring disease (anatomical) locations from their use as subject labels in journal articles. Our box model substantially outperforms all baselines for taxonomic reconstruction and bipartite relationship experiments. This performance improvement is observed both in overall accuracy and the weighted spread by true taxonomic depth.