  The correlated polar semimetal Ca$_3$Ru$_2$O$_7$ exhibits a rich phase
diagram including two magnetic transitions ($T_N$=56 K and $T_C$=48 K) with the
appearance of an insulating-like pseudogap (at $T_C$). In addition, there is a
crossover back to metallic behavior at $T^*$=30 K, the origin of which is still
under debate. We utilized ultrafast optical pump optical probe spectroscopy to
investigate quasiparticle dynamics as a function of temperature in this
enigmatic quantum material. We identify two dynamical processes, both of which
are influenced by the onset of the pseudogap. This includes electron-phonon
relaxation and, below $T_C$, the onset of a phonon bottleneck hindering the
relaxation of quasiparticles across the pseudogap. We introduce a gap-modified
two-temperature model to describe the temperature dependence of electron-phonon
thermalization, and use the Rothwarf-Taylor to model the phonon bottleneck. In
conjunction with density functional theory, our experimental results
synergistically reveal the origin of the $T$-dependent pseudogap. Further, our
data and analysis indicate that $T^*$ emerges as a natural consequence of
$T$-dependent gapping out of carriers, and does not correspond to a separate
electronic transition. Our results highlight the value of low fluence ultrafast
optics as a sensitive probe of low energy electronic structure, thermodynamic
parameters, and transport properties of Ruddlesden-Popper ruthenates.
