We examine the left-right asymmetry in the cleaned COBE/DIRBE near-infrared data of the inner Galaxy and show (i) that the Galactic bar is probably not seen very nearly end-on, and (ii) that even if it is, it is not highly elongated. The assumption of constant mass-to-light ratio is used to derive simulated terminal-velocity plots for the ISM from our model luminosity distributions. By comparing these plots with observed terminal velocities we determine the mass-to-light ratio of the near-IR bulge and disk. Assuming that all this mass contributes to gravitational microlensing we compute optical depths $tau$ for microlensing in Galactic-centre fields. For three models with bar major axis between $10deg-25deg$ from the Sun-Galactic Center line, the resulting optical depths in Baades window lie in the range $0.83times10^{-6} lta tau lta 0.89times10^{-6}$ for main-sequence stars and $1.2times10^{-6} lta tau lta 1.3times10^{-6}$ for red-clump giants. We discuss a number of uncertainties including possible variations of the near-infrared mass-to-light ratio. We conclude that, although the values predicted from analyzing the COBE and gas velocity data are inconsistent at the $2-2.5sigma$ level with recent observational determinations of $tau$, we believe they should be taken seriously.
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