We utilize the Sagittarius Window Eclipsing Extrasolar Planet Search Hubble Space Telescope/Advanced Camera for Surveys data set for a Deep Rapid Archival Flare Transient Search (DRAFTS) to constrain the flare rate toward the older stellar population in the Galactic bulge. During seven days of monitoring 229293 stars brighter than V=29.5, we find evidence for flaring activity in 105 stars between V=20 and V=28. We divided the sample into non-variable stars and variable stars whose light curves contain large-scale variability. The flare rate on variable stars is ~700 times that of non-variable stars, with a significant correlation between the amount of underlying stellar variability and peak flare amplitude. The flare energy loss rates are generally higher than those of nearby well-studied single dMe flare stars.