Multi-host pathogens are particularly difficult to control, especially when at least one of the hosts acts as a hidden reservoir. Deep sequencing of densely sampled pathogens has the potential to transform this understanding, but requires analytical approaches that jointly consider epidemiological and genetic data to best address this problem. While there has been considerable success in analyses of single species systems, the hidden reservoir problem is relatively under-studied. A well-known exemplar of this problem is bovine Tuberculosis, a disease found in British and Irish cattle caused by Mycobacterium bovis, where the Eurasian badger has long been believed to act as a reservoir but remains of poorly quantified importance except in very specific locations. As a result, the effort that should be directed at controlling disease in badgers is unclear. Here, we analyse densely collected epidemiological and genetic data from a cattle population but do not explicitly consider any data from badgers. We use a simulation modelling approach to show that, in our system, a model that exploits available cattle demographic and herd-to-herd movement data, but only considers the ability of a hidden reservoir to generate pathogen diversity, can be used to choose between different epidemiological scenarios. In our analysis, a model where the reservoir does not generate any diversity but contributes to new infections at a local farm scale are significantly preferred over models which generate diversity and/or spread disease at broader spatial scales. While we cannot directly attribute the role of the reservoir to badgers based on this analysis alone, the result supports the hypothesis that under current cattle control regimes, infected cattle alone cannot sustain M. bovis circulation. Given the observed close phylogenetic relationship for the bacteria taken from cattle and badgers sampled near to each other, the most parsimonious hypothesis is that the reservoir is the infected badger population. More broadly, our approach demonstrates that carefully constructed bespoke models can exploit the combination of genetic and epidemiological data to overcome issues of extreme data bias, and uncover important general characteristics of transmission in multi-host pathogen systems.