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 active galactic nucleus (AGN) activity over the past decade. With a redshift of z = 0.01107 and a peak ultraviolet (UV)/optical luminosity of (5.4 ±0.4) ×1042 erg s-1, ASASSN-23bd is the lowest-redshift and least-luminous TDE disco v ered to date. Spectroscopically, ASASSN-23bd shows H α and He I emission throughout its spectral time series, there are no coronal lines in its near-infrared spectrum, 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, ~9 d before disco very, with a nearly linear rise in flux, peaking in the g band on MJD 60 000+3-3. Scaling relations and TDE light curve modelling find a black hole mass of ~106 M⊙, which is on the lower end of supermassive black hole masses. ASASSN-23bd is a dim X-ray source, with an upper limit of L0.3-10keV < 1.0 ×1040 erg s-1 from stacking all Swift observations prior to MJD 60061, but with soft (~0.1 keV) thermal emission with a luminosity of L0.3-2keV ~4 ×1039 erg s-1 in XMM-Newton observations on MJD 60095. The rapid (t < 15 d) light curve rise, low UV/optical luminosity, and a luminosity decline over 40 d of ΔL40 ≈-0.7 dex make ASASSN-23bd one of the dimmest TDEs to date and a member of the growing 'Low Luminosity and Fast' class of TDEs.