We present a combined oxygen K-edge x-ray absorption spectroscopy and resonant inelastic x-ray scattering (RIXS) study of the bilayer ruthenate Ca3Ru2O7. Our RIXS experiments on Ca3Ru2O7 were carried out on the overlapping planar and interplanar oxygen resonances, which are distinguishable from the apical one. Comparison to equivalent oxygen K-edge spectra recorded on band-Mott insulating Ca2RuO4 is made. In contrast to Ca2RuO4 spectra, which contain excitations linked to Mott physics, Ca3Ru2O7 spectra feature only intra-t(2g) ones that do not directly involve the Coulomb energy scale. As found in Ca2RuO4, we resolve two intra-t(2g) excitations in Ca3Ru2O7. Moreover, the lowest lying excitation in Ca3Ru2O7 shows a significant dispersion, revealing a collective character different from what is observed in Ca2RuO4. Theoretical modeling supports the interpretation of this lowest energy excitation in Ca3Ru2O7 as a magnetic transverse mode with multiparticle character, whereas the corresponding excitation in Ca2RuO4 is assigned to combined longitudinal and transverse spin modes. These fundamental differences are discussed in terms of the inequivalent magnetic ground-state manifestations in Ca2RuO4 and Ca3Ru2O7.