OGLE-2003-BLG-262: Finite-source effects from a point-mass lens

We analyze OGLE-2003-BLG-262, a relatively short (t(E)=12.5+/-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+/-17 muas, and so constrain the lens mass to the FWHM interval 0.08<M/M-circle dot<0.54. The lens-source relative proper motion is mu(rel)=27 +/- 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.