The Zwicky Transient Facility (ZTF) is performing a three-day cadence survey of the visible Northern sky (~3$pi$). The transient candidates found in this survey are announced via public alerts. As a supplementary product ZTF is also conducting a large spectroscopic campaign: the ZTF Bright Transient Survey (BTS). The goal of the BTS is to spectroscopically classify all extragalactic transients brighter than 18.5 mag at peak brightness and immediately announce those classifications to the public. Extragalactic discoveries from ZTF are predominantly Supernovae (SNe). The BTS is the largest flux-limited SN survey to date. Here we present a catalog of the761 SNe that were classified during the first nine months of the survey (2018 Apr. 1 to 2018 Dec. 31). The BTS SN catalog contains redshifts based on SN template matching and spectroscopic host galaxy redshifts when available. Based on this data we perform an analysis of the redshift completeness of local galaxy catalogs, dubbed as the Redshift Completeness Fraction (RCF; the number of SN host galaxies with known spectroscopic redshift prior to SN discovery divided by the total number of SN hosts). In total, we identify the host galaxies of 512 Type Ia supernovae, 227 of which have known spectroscopic redshifts, yielding an RCF estimate of $44% pm1%$. We find a steady decrease in the RCF with increasing distance in the local universe. For z<0.05, or ~200 Mpc, we find RCF=0.6, which has important ramifications when searching for multimessenger astronomical events. Prospects for dramatically increasing the RCF are limited to new multi-fiber spectroscopic instruments, or wide-field narrowband surveys. We find that existing galaxy redshift catalogs are only $50%$ complete at $rapprox16.9$ mag. Pushing this limit several magnitudes deeper will pay huge dividends when searching for electromagnetic counterparts to gravitational wave events.