Bathymetry beneath ice shelves in West Antarctica plays an important role in the delivery and circulation of warm waters to the ice-shelf bottom and grounding line. Large-scale bathymetric estimates can only be inferred through inversion of airborne gravity measurements. However, previous bathymetry inversions have not robustly quantified uncertainty in the bathymetry due to assumptions inherent in the inversion, and typically only produce a single model, making it difficult to propagate uncertainty into ocean and ice-sheet models. Previous inversions have sometimes considered uncertainties in bathymetry models due to background densities but have not quantified the uncertainty due to the non-uniqueness inherent in gravity and geological variability below ice shelves. To address these issues, we develop a method to generate ensembles of bathymetry models beneath the Crosson, Dotson, and Thwaites Eastern ice shelves with independent realizations of background density and geological variability, represented through the Bouguer gravity disturbance. We sample the uncertainty in the unknown geology below the ice shelves by interpolating the Bouguer disturbance using Sequential Gaussian Simulation. Each inversion is efficiently solved using a random walk Metropolis Markov Chain Monte Carlo approach which randomly updates blocks of bathymetry and accepts or rejects updates. Our ensembles of bathymetry models differ from previous estimates of bathymetry by hundreds of meters in some areas and show that the uncertainty in the Bouguer disturbance is the largest source of uncertainty. The different bathymetry models in the ensembles can be used in oceanographic models to place better bounds on sub-ice-shelf melting and future grounding line retreat.