Hot, underdense bubbles powered by active galactic nuclei (AGN) are likely to play a keyrole in halting catastrophic cooling in the centers of cool-core galaxy clusters. Wepresent three-dimensional simulations that capture the evolution of such bubbles, using anadaptive-mesh hydrodynamic code, FLASH3, to which we have added a subgrid model ofturbulence and mixing. Pure-hydro simulations indicate that AGN bubbles are disrupted intoresolution-dependent pockets of underdense gas. However, proper modeling of subgridturbulence shows that Rayleigh-Taylor instabilities act to mix the heated regions withtheir surroundings, while at the same time preserving them as coherent structures,consistent with observations. Thus bubbles are transformed into hot clouds of mixedmaterial as they move outwards in the hydrostatic intracluster medium. Properly capturingthe evolution of such clouds has important implications for many ICM properties.