  In the spin ladder compound BiCu$_2$PO$_6$ there exists a decisive dynamics
of spin excitations that we classify and characterize using inelastic light
scattering. We observe low-energy singlets and a broad triplon continuum
extending from 36 cm$^{-1}$ to 700 cm$^{-1}$ in ($aa$), ($bb$), and ($cc$)
light scattering polarizations. Though isolated spin ladder physics can roughly
account for the observed excitations at high energies, frustration and
interladder interactions need to be considered to fully describe the spectral
distribution and scattering selection rules at low and intermediate energies.
More significantly, an interladder singlet bound mode at 24 cm$^{-1}$, lying
below the continuum, shows its largest scattering intensity in interladder
($ab$) polarization. In contrast, two intraladder bound states at 62 cm$^{-1}$
and 108 cm$^{-1}$ with energies comparable to the continuum are observed with
light polarization along the leg ($bb$) and the rung ($cc$). We attribute the
rich spectrum of singlet bound modes to a melting of a dimer crystal. Our study
provides evidence for a Z$_2$ quantum phase transition from a dimer to a
resonating valence bond state driven by singlet fluctuations.
