Bathymetry beneath ice shelves is challenging to observe yet is vitally important for modelling how ice sheets will evolve into the future. An alternative to direct observation of bathymetry is to invert airborne gravity data for the bathymetric signal. Appropriate gravity data can be collected via remote sensing above the ice shelf and be used to provide an initial estimate of sub-ice-shelf bathymetry, typically at wavelengths of ~5 km and above. However, lateral variations in density associated with the underlying geology can distort the gravity field biassing the results. We show that techniques which tie inversion results to known bathymetry and topography, although solving some of these issues, may be insufficient in the case of large and deep basins lacking centrally located tie points. Using new direct observations of the Dotson and Crosson ice shelves as a case study, we show that gravity inversion for bathymetry can be improved by considering and removing a model of the gravity field due to crustal isostatic compensation prior to inversion. We finally present our updated and improved bathymetric model for the Dotson-Crosson and Thwaites Glacier Ice Shelf system and discuss where our method can be best applied in future.