  The CO-to-H$_2$ conversion factor ($\alpha_\rm{CO}$) is critical to studying
molecular gas and star formation in galaxies. The value of $\alpha_\rm{CO}$ has
been found to vary within and between galaxies, but the specific environmental
conditions that cause these variations are not fully understood. Previous
observations on $\sim$kpc scales revealed low values of $\alpha_\rm{CO}$ in the
centers of some barred spiral galaxies, including NGC 3351. We present new ALMA
Band 3, 6, and 7 observations of $^{12}$CO, $^{13}$CO, and C$^{18}$O lines on
100 pc scales in the inner $\sim$2 kpc of NGC 3351. Using multi-line radiative
transfer modeling and a Bayesian likelihood analysis, we infer the H$_2$
density, kinetic temperature, CO column density per line width, and CO
isotopologue abundances on a pixel-by-pixel basis. Our modeling implies the
existence of a dominant gas component with a density of $2{-}3\times10^3$
$\rm{cm^{-3}}$ in the central ${\sim}$1 kpc and a high temperature of 30$-$60 K
near the nucleus and near the contact points that connect to the bar-driven
inflows. Assuming a CO/H$_2$ abundance of $3\times10^{-4}$, our analysis yields
$\alpha_\rm{CO}{\sim}0.5{-}2.0$ $\rm{M_\odot\,(K~km~s^{-1}~pc^2)^{-1}}$ with a
decreasing trend with galactocentric radius in the central $\sim$1 kpc. The
inflows show a substantially lower $\alpha_\rm{CO} < 0.1$
$\rm{M_\odot\,(K~km~s^{-1}~pc^2)^{-1}}$, likely due to lower optical depths
caused by turbulence or shear in the inflows. Over the whole region, this gives
an intensity-weighted $\alpha_\rm{CO}$ of ${\sim}1.5$
$\rm{M_\odot\,(K~km~s^{-1}~pc^2)^{-1}}$, which is similar to previous dust
modeling based results at kpc scales. This suggests that low $\alpha_\rm{CO}$
on kpc scales in the centers of some barred galaxies may be due to the
contribution of low optical depth CO emission in bar-driven inflows.
