The quarantining of Ebola virus disease (EVD) infectious individuals in hospitals and controlled environments largely depends on the availability of unoccupied habitable beds in the hospitals and environments. This work addresses the role of limited hospitalisation on the transmission of EVD using a unique compartmental model incorporating hospital beds’ dynamics within the hospital compartment. We consider a bed-dependent hospitalisation function and assume that although the bed growth rate is logistic in nature, it only occurs via the refurbishment of unhabitable beds. The epidemic threshold, the conditions for the local stability of the disease-free equilibrium, and the existence of a backward bifurcation in the system are determined. The model is fitted to data from the Democratic Republic of Congo (DRC) and sensitivity analysis is carried out to determine important parameters that should be targeted when considering interventions. Our results suggest that in the case of an EVD outbreak, unhabitable beds should be continually refurbished if the disease must be contained.