We conduct a quantitative analysis of the star formation history ( SFH ) of the Milky Way ’ s bulge by exploiting the constraining power of its stellar [ Fe/H ] and [ Mg/Fe ] distribution functions . Using APOGEE data , we confirm the previously-established bimodal [ Mg/Fe ] – [ Fe/H ] distribution within 3 kpc of the inner Galaxy . Compared to that in the solar vicinity , the high- \alpha population in the bulge peaks at a lower [ Fe/H ] . To fit these observations , we use a simple but flexible star formation framework , which assumes two distinct stages of gas accretion and star formation , and systematically evaluate a wide multi-dimensional parameter space . We find that the data favor a three-phase SFH that consists of an initial starburst , followed by a rapid star formation quenching episode and a lengthy , quiescent secular evolution phase . The metal-poor , high- \alpha bulge stars ( [ Fe/H ] < 0.0 and [ Mg/Fe ] > 0.15 ) are formed rapidly ( < 2 Gyr ) during the early starburst . The density gap between the high- and low- \alpha sequences is due to the quenching process . The metal-rich , low- \alpha population ( [ Fe/H ] > 0.0 and [ Mg/Fe ] < 0.15 ) then accumulates gradually through inefficient star formation during the secular phase . This is qualitatively consistent with the early SFH of the inner disk . Given this scenario , a notable fraction of young stars ( age < 5 Gyr ) is expected to persist in the bulge . Combined with extragalactic observations , these results suggest that a rapid star formation quenching process is responsible for bimodal distributions in both the MW’s stellar populations and in the general galaxy population and thus plays a critical role in galaxy evolution .