We report the detection of 45 candidate microlensing events in fields toward the Galactic bulge. These come from the analysis of 24 fields containing 12.6 million stars observed for 190 days in 1993. Many of these events are of extremely high signal to noise and are remarkable examples of gravitational microlensing. The distribution of peak magnifications is shown to be consistent with the microlensing interpretation of these events. Using a sub-sample of 1.3 million ``Clump Giant stars whose distance and detection efficiency are well known, we find 13 events and estimate the microlensing optical depth toward the Galactic Bulge as $tau_{rm bulge} = 3.9 {+ 1.8 atop - 1.2} times 10^{-6}$ averaged over an area of $sim 12$ square degrees centered at Galactic coordinates $ell = 2.55^circ$ and $b = -3.64^circ$. This is similar to the value reported by the OGLE collaboration, and is marginally higher than current theoretical models for $tau_{rm bulge}$. The optical depth is also seen to increase significantly for decreasing $vert bvert$. These results demonstrate that obtaining large numbers of microlensing events toward the Galactic bulge is feasible, and that the study of such events will have important consequences for the structure of the Galaxy and its dark halo.