  Many polyatomic astrophysical plasmas are compressible and out of chemical
and thermal equilibrium, and yet, due to Stokes' hypothesis, a means to
carefully control the decay of compressible modes in these systems has largely
been neglected. This is especially important for small-scale, turbulent dynamo
processes, which are known to be sensitive to the effects of compression. To
control the viscous properties of the compressible modes, we perform
supersonic, visco-resistive dynamo simulations with additional bulk viscosity
$\nu_{\rm bulk}$, deriving a new $\nu_{\rm bulk}$ Reynolds number $\rm{Re}_{\rm
bulk}$, and viscous Prandtl number $\rm{P}\nu \equiv \rm{Re}_{\rm bulk} /
\rm{Re}_{\rm shear}$, where $\rm{Re}_{\rm shear}$ is the shear viscosity
Reynolds number. For $10^{-3} \leq \rm{P}\nu \leq \infty$, we explore a broad
range of statistics critical to the dynamo problem, including the integral and
spectral energy ratios, growth rates, and the magnetic $E_{\rm mag}(k)$ and
kinetic $E_{\rm kin}(k)$ energy spectrum. We derive a general framework for
decomposing $E_{\rm mag}$ growth rates into incompressible and compressible
terms via orthogonal tensor decompositions of $\nabla\otimes\mathbf{v}$, where
$\mathbf{v}$ is the fluid velocity. We find that compressible modes play a dual
role, growing and decaying $E_{\rm mag}$, and that field-line stretching is the
main driver of growth, even in supersonic dynamos. In the absence of $\nu_{\rm
bulk}$, compressible modes pile up on small-scales, creating an apparent
spectral bottleneck, which disappears for $\rm{P}\nu \approx 1$. As $\rm{P}\nu$
decreases, compressible modes are dissipated at increasingly larger scales, in
turn suppressing incompressible modes through a coupling between viscosity
operators. We emphasise the importance of further understanding the role of
$\nu_{\rm bulk}$ in compressible astrophysical plasmas.
