We investigate the polaronic ground state of anatase TiO2 by bulk-sensitive resonant inelastic x-ray spectroscopy (RIXS) at the Ti L-3 edge. We find that the formation of the polaron cloud involves a single 95 meV phonon along the c axis, in addition to the 108 meV ab-plane mode previously identified by photoemission. The coupling strength to both modes is the same within error bars, and it is unaffected by the carrier density. These data establish RIXS as a directional bulk-sensitive probe of electron-phonon coupling in solids.