We utilize the Sagittarius Window Eclipsing Extrasolar Planet Search (SWEEPS) HST/ACS dataset for a Deep Rapid Archival Flare Transient Search (DRAFTS) to constrain the flare rate toward the older stellar population in the Galactic bulge. During 7 days of monitoring 229,293 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. The distribution of proper motions is consistent with the flaring stars being at the distance and age of the Galactic bulge. If they are single dwarfs, they span a range of ≈ 1.0 − 0.25M ⊙ . A majority of the flaring stars exhibit periodic photometric modulations with P <3d. If these are tidally locked magnetically active binary systems, their fraction in the bulge is enhanced by a factor of ∼20 compared to the local value. These stars may be useful for placing constraints on the angular momentum evolution of cool close binary stars. Our results expand the type of stars studied for flares in the optical band, and suggest that future sensitive optical time-domain studies will have to contend with a larger sample of flaring stars than the M dwarf flare stars usually considered.Recent results from searches for deep optical fast (<1 hr) transients have indicated the prevalence of stellar flaring and bolstered support for a better quantification of the flare rate. The three transients identified in Becker et al. (2004) turned out to be Galactic flare stars; Kulkarni & Rau (2006) described this population as a foreground "fog" potentially obscuring extragalactic fast optical transients (timescales of ≈1000 s). Fresneau et al. (2001) reported results from an astrographic plate survey at low galactic latitude, covering a large field of view (520 degrees 2 ) at B magnitudes between 10 and 14; 8% of stars showed flare events greater than 0.4 mag over 20-30 minute timescales. Ramsay & Hakala (2005) performed sensitive but shallow temporal coverage observations at intermediate galactic latitude, reaching depths of