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We present stellar age distributions of the Milky Way (MW) bulge region using ages for $\sim$6,000 high-luminosity ($\log(g) < 2.0$), metal-rich ($\rm [Fe/H] \ge -0.5$) bulge stars observed by the Apache Point Observatory Galactic Evolution Experiment (APOGEE). Ages are derived using {\it The Cannon} label-transfer method, trained on a sample of nearby luminous giants with precise parallaxes for which we obtain ages using a Bayesian isochrone-matching technique. We find that the metal-rich bulge is predominantly composed of old stars ($>$8 Gyr). We find evidence that the planar region of the bulge ($|Z_{\rm GC}| \le 0.25$ kpc) enriched in metallicity, $Z$, at a faster rate ($dZ/dt \sim$ 0.0034 ${\rm Gyr^{-1}}$) than regions farther from the plane ($dZ/dt \sim$ 0.0013 ${\rm Gyr^{-1}}$ at $|Z_{\rm GC}| > 1.00$ kpc). We identify a non-negligible fraction of younger stars (age $\sim$ 2--5 Gyr) at metallicities of $\rm +0.2 < [Fe/H] < +0.4$. These stars are preferentially found in the plane ($|Z_{\rm GC}| \le 0.25$ kpc) and between $R_{\rm cy} \approx 2-3$ kpc, with kinematics that are more consistent with rotation than are the kinematics of older stars at the same metallicities. We do not measure a significant age difference between stars found in and outside of the bar. These findings show that the bulge experienced an initial starburst that was more intense close to the plane than far from the plane. Then, star formation continued at super-solar metallicities in a thin disk at 2 kpc $\lesssim R_{\rm cy} \lesssim$ 3 kpc until $\sim$2 Gyr ago.