We report x-ray photoemission spectroscopy results on (Ga,Mn)As films as a function of both temperature and Mn doping. Analysis of Mn 2p core level spectra reveals the presence of a distinct electronic screening channel in the bulk, hitherto undetected in more surface sensitive analysis. Comparison with model calculations identifies the character of the Mn 3d electronic states and clarifies the role, and the difference between surface and bulk, of hybridization in mediating the ferromagnetic coupling in (Ga,Mn)As.