  We use Ru $L_3$-edge resonant inelastic x-ray scattering (RIXS) to study the
full range of excitations in Ca$_3$Ru$_2$O$_7$ from meV-scale magnetic dynamics
through to the eV-scale interband transitions. This bilayer $4d$-electron
correlated metal expresses a rich phase diagram, displaying long range magnetic
order below 56 K followed by a concomitant structural, magnetic and electronic
transition at 48 K. In the low temperature phase we observe a magnetic
excitation with a bandwidth of $\sim$30 meV and a gap of $\sim$8 meV at the
zone center, in excellent agreement with inelastic neutron scattering data. The
dispersion can be modeled using a Heisenberg Hamiltonian for a bilayer
$\mathrm{S}=1$ system with single ion anisotropy terms. At a higher energy
loss, $dd$-type excitations show heavy damping in the presence of itinerant
electrons, giving rise to a fluorescence-like signal appearing between the
$t_{2g}$ and $e_g$ bands. At the same time, we observe a resonance originating
from localized $t_{2g}$ excitations, in analogy to the structurally related
Mott-insulator Ca$_2$RuO$_4$. But whereas Ca$_2$RuO$_4$ shows sharp separate
spin-orbit excitations and Hund's-rule driven spin-state transitions, here we
identify only a single broad asymmetric feature. These results indicate that
local intra-ionic interactions underlie the correlated physics in
Ca$_3$Ru$_2$O$_7$, even as the excitations become strongly mixed in the
presence of itinerant electrons.
