We analyze OGLE-2003-BLG-262, a relatively short, t_E=12.5+-0.1day, microlensing event generated by a point-mass lens transiting the face of a K giant source in the Galactic bulge. We use the resulting finite-source effects to measure the angular Einstein radius, theta_E=195+-17muas, and so constrain the lens mass to the full-width half-maximum interval 0.08 < M/M_sun < 0.54. The lens-source relative proper motion is mu_rel = 27+-2 km/s/kpc. Both values are typical of what is expected for lenses detected toward the bulge. Despite the short duration of the event, we detect marginal evidence for a parallax asymmetry, but argue that this is more likely to be induced by acceleration of the source, a binary lens, or possibly by statistical fluctuations. Although OGLE-2003-BLG-262 is only the second published event to date in which the lens transits the source, such events will become more common with the new OGLE-III survey in place. We therefore give a detailed account of the analysis of this event to facilitate the study of future events of this type.
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