We report on observations of the stellar populations in 12 fields spanning the region between the Magellanic Clouds, made with the Mosaic II camera on the 4m telescope at the Cerro-Tololo Inter-American Observatory. The two main goals of the observations are to characterize the young stellar population (which presumably formed in situ in the Bridge and therefore represents the nearest stellar population formed from tidal debris), and to search for an older stellar component (which would have been stripped from either Cloud as stars, by the same tidal forces that formed the gaseous Bridge). We determine the star formation history of the young inter-Cloud population, which provides a constraint on the timing of the gravitational interaction that formed the Bridge. We do not detect an older stellar population belonging to the Bridge in any of our fields, implying that the material that was stripped from the Clouds to form the Magellanic Bridge was very nearly a pure gas.