We analyze OGLE-2003-BLG-262 , a relatively short , t _ { E } = 12.5 \pm 0.1 day , 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 \pm 17 { \mu as } , and so constrain the lens mass to the full-width half-maximum interval 0.08 < M / M _ { \odot } < 0.54 . The lens-source relative proper motion is \mu _ { rel } = 27 \pm 2 { km } { s } ^ { -1 } { kpc } ^ { -1 } . 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 .