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We present a bar-informed kinematic-distance (BIKD) method to reconstruct face-on molecular-gas maps of the inner Milky Way from PPV data, relaxing the standard assumption of axisymmetric circular rotation that can generate severe artifacts in barred regions. BIKD replaces the rotation curve with a non-axisymmetric streaming field extracted from hydrodynamical simulations in an observationally constrained barred Galactic potential, and infers a discrete distance posterior along each sightline using a Gaussian likelihood in line-of-sight velocity. To mitigate multi-modality, we adopt posterior-weighted map making via posterior sampling. We validate the full pipeline in closed-loop tests on the simulations, showing that the recovered large-scale morphology is only weakly sensitive to simple distance priors and remains stable across plausible variations in bar angle, snapshot time, and pattern speed. We then apply BIKD to a Galactic CO survey to obtain a face-on $Σ$ map. Compared to a standard axisymmetric kinematic-distance (KD) reconstruction, BIKD strongly suppresses line-of-sight--elongated finger-of-God features and robustly recovers a bar-aligned, quadrant-asymmetric inner-Galaxy morphology under model marginalization. The model-marginalized radial profiles show an approximately exponential decline beyond $\sim4$ kpc, a pronounced deficit at $R\sim0.5$--$3.5$ kpc, and a central concentration consistent with Central Molecular Zone surface densities. Finally, we compare prominent ridge-shaped overdensities in the BIKD map with independent spiral-arm loci traced by high-mass star-forming region masers with VLBI trigonometric parallaxes and by classical Cepheids with period--luminosity distances. Several maser-parallax segments are qualitatively consistent with the dominant BIKD ridges, whereas the Cepheid loci do not coincide with them within their recommended azimuth range.