  Tidal disruption events (TDEs) provide a means to probe the low end of the
supermassive black hole (SMBH) mass distribution, as they are only observable
below the Hills mass ($\lesssim 10^8$ M$_\odot$). Here we attempt to calibrate
the scaling of SMBH mass with host galaxy bulge mass, enabling SMBH masses to
be estimated for large TDE samples without the need for follow-up observations
or extrapolations of relations based on high-mass samples. We derive host
galaxy masses using Prospector fits to the UV-MIR spectral energy distributions
for the hosts of 29 well-observed TDEs with BH mass estimates from MOSFiT. We
then conduct detailed bulge/disk decomposition using SDSS and PanSTARRS
imaging, and provide a catalog of bulge masses. We measure a positive
correlation between SMBH and bulge mass for the TDE sample, with a power-law
slope of 0.28 and significance $p=0.06$ (Spearmans) and $p=0.05$ (Pearsons),
and an intrinsic scatter of 0.2 dex. Applying MC resampling and bootstrapping,
we find a more conservative estimate of the slope is $0.18\pm0.11$, dominated
by the systematic errors from Prospector and MOSFiT. This is shallower than the
slope at high SMBH mass, which may be due to a bias in the TDE sample towards
lower mass BHs that can more easily disrupt low-mass stars outside of the event
horizon. When combining the TDE sample with that of the high mass regime, we
find that TDEs are successful in extending the SMBH - stellar mass relationship
further down the mass spectrum and provide a relationship across the full range
of SMBH masses.
