The mass transport of gallium adatoms in a confined gallium bilayer on GaN(0001) is studied with photoelectron spectromicroscopy with the goal to identify the diffusing species and their lateral distribution during directional surface electromigration and/or "random" thermal diffusion. It has been found that only the gallium atoms from the second layer undergo biased diffusion involving formation of three-dimensional islands. The development of different gallium concentration patterns is described by means of a general model, considering the presence of vacancies and trapping centres for the diffusing atoms.