Gas–liquid systems involving dispersed bubbly flows are often encountered in industry due to their favourable heat and mass transport characteristics. A key element of such systems involving interfacial mass transfer are the thin mass boundary layers prevailing at the phase boundaries. Resolving these thin boundary layers in numerical simulations is very challenging because of the need for very fine grids. Such grids often over-resolve the hydrodynamics which accounts for most of the CPU time. In this paper, we propose a multiple resolution approach that resolves the momentum boundary layers on a coarse (fixed) Cartesian grid and the mass boundary layers on a finer (adaptive) grid. The methodology proposed in Panda et al. (2019) for static rigid particles is extended to deformable moving interfaces and applied to single rising bubbles where the computed Sherwood number is compared with empirical correlations and numerical simulations available in literature.