We present the results of a new, wide-field, and broad-ranging survey for 12CO (1-0) emission regions in the nearest and brightest tidal structure: the Magellanic Bridge. We have detected seven sites of 12CO (1-0) emission using the NANTEN telescope in addition to the one detected previously. The integrated CO brightness for these detections ranges between 30 and 140 mK km s-1, corresponding to an estimated molecular mass of (1-7) × 103 M☉ [assuming the CO-to-H2 conversion factor (X-factor) of ~1.4 × 1021 cm-2 (K km s-1)-1]. The positions of the CO emission regions are generally coincident with sites of bright 100 μm emission, where I100 μm > 2.6 MJy sr-1, and have narrow line widths of <~2 km s-1, indicating gas in a cold and rather quiescent state. The velocity centroids of the CO spectra are generally consistent with those of the H I spectra, and we suggest that CO clouds are formed after the tidal encounter, rather than being extracted from the SMC. This is supported by the small typical lifetime of CO clouds, which is as short as ~107 yr and much less than the estimated 200 Myr age of the Bridge itself.