The HST/WFC3 multiband photometry spanning from the UV to the near-IR of four fields in the Galactic bulge, together with that for six template globular and open clusters, are used to photometrically tag the metallicity [Fe/H] of stars in these fields after proper-motion rejecting most foreground disk contaminants. Color-magnitude diagrams and luminosity functions are then constructed, in particular for the most metal rich and most metal poor stars in each field. We do not find any significant difference between the $I$-band and $H$-band luminosity functions, hence turnoff luminosity and age, of the metal rich and metal poor components which therefore appear essentially coeval. In particular, we find that no more than $sim 3%$ of the metal-rich component can be $sim 5$ Gyr old, or younger. Conversely, theoretical luminosity functions give a good match to the observed ones for an age of ~10 Gyr. Assuming this age is representative for the bulk of bulge stars, we then recall the observed properties of star-forming galaxies at 10 Gyr lookback time, i.e., at z~2, and speculate about bulge formation in that context. We argue that bar formation and buckling instabilities leading to the observed boxy/peanut, X-shaped bulge may have arisen late in the history of the Milky Way galaxy, once its gas fraction had decreased compared to the high values typical of high-redshift galaxies. This paper follows the public release of the photometric and astrometric catalogs for the measured stars in the four fields.
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