  We report the All-Sky Automated Survey for SuperNovae discovery of the tidal
disruption event (TDE) ASASSN-23bd (AT 2023clx) in NGC 3799, a LINER galaxy
with no evidence of strong AGN activity over the past decade. With a redshift
of $z = 0.01107$ and a peak UV/optical luminosity of $(5.4\pm0.4)\times10^{42}$
erg s$^{-1}$, ASASSN-23bd is the lowest-redshift and least-luminous TDE
discovered to date. Spectroscopically, ASASSN-23bd shows H$\alpha$ and He I
emission throughout its spectral time series, and the UV spectrum shows
nitrogen lines without the strong carbon and magnesium lines typically seen for
AGN. Fits to the rising ASAS-SN light curve show that ASASSN-23bd started to
brighten on MJD 59988$^{+1}_{-1}$, $\sim$9 days before discovery, with a nearly
linear rise in flux, peaking in the $g$ band on MJD $60000^{+3}_{-3}$. Scaling
relations and TDE light curve modelling find a black hole mass of $\sim$10$^6$
$M_\odot$, which is on the lower end of supermassive black hole masses.
ASASSN-23bd is a dim X-ray source, with an upper limit of
$L_{0.3-10\,\mathrm{keV}} < 1.0\times10^{40}$ erg s$^{-1}$ from stacking all
\emph{Swift} observations prior to MJD 60061, but with soft ($\sim 0.1$ keV)
thermal emission with a luminosity of $L_{0.3-2
\,\mathrm{keV}}\sim4\times10^{39}$ erg s$^{-1}$ in \emph{XMM-Newton}
observations on MJD 60095. The rapid $(t < 15$ days) light curve rise, low
UV/optical luminosity, and a luminosity decline over 40 days of $\Delta
L_{40}\approx-0.7$ make ASASSN-23bd one of the dimmest TDEs to date and a
member of the growing ``Low Luminosity and Fast'' class of TDEs.
