  We present the probabilistic stellar mass function (pSMF) of galaxies in the
DESI Bright Galaxy Survey (BGS), observed during the One-Percent Survey. The
One-Percent Survey was one of DESI's survey validation programs conducted from
April to May 2021, before the start of the main survey. It used the same target
selection and similar observing strategy as the main survey and successfully
observed the spectra and redshifts of 143,017 galaxies in the $r < 19.5$
magnitude-limited BGS Bright sample and 95,499 galaxies in the fainter surface
brightness and color selected BGS Faint sample over $z < 0.6$. We derive pSMFs
from posteriors of stellar mass, $M_*$, inferred from DESI photometry and
spectroscopy using the Hahn et al. (2022a; arXiv:2202.01809) PRObabilistic
Value-Added BGS (PROVABGS) Bayesian SED modeling framework. We use a
hierarchical population inference framework that statistically and rigorously
propagates the $M_*$ uncertainties. Furthermore, we include correction weights
that account for the selection effects and incompleteness of the BGS
observations. We present the redshift evolution of the pSMF in BGS as well as
the pSMFs of star-forming and quiescent galaxies classified using average
specific star formation rates from PROVABGS. Overall, the pSMFs show good
agreement with previous stellar mass function measurements in the literature.
Our pSMFs showcase the potential and statistical power of BGS, which in its
main survey will observe >100$\times$ more galaxies. Moreover, we present the
statistical framework for subsequent population statistics measurements using
BGS, which will characterize the global galaxy population and scaling relations
at low redshifts with unprecedented precision.
