Context. Recent observational programs are providing a global view of the Milky Way bulge that serves as a template for detailed comparison with models and extragalactic bulges. A number of surveys (VVV, GIBS, GES, ARGOS, BRAVA, APOGEE) are producing comprehensive and detailed extinction, metallicity, kinematics, and stellar density maps of the Galactic bulge with unprecedented accuracy. However, the still missing key ingredient is the distribution of stellar ages across the bulge. Aims: To overcome this limitation, we aim to age-date the stellar population in several bulge fields with the ultimate goal of deriving an age map of the bulge. This paper presents the methodology and the first results obtained for a field along the bulge minor axis, at b = -6°. Methods: We use a new PSF-fitting photometry of the VISTA Variables in the Vía Láctea (VVV) survey data to construct deep color-magnitude diagrams of the bulge stellar population down to ˜2 mag below the main sequence turnoff. To address the contamination by foreground disk stars we adopt a statistical approach by using control-disk fields located at different latitudes (spanning approximately the bulge's range) and longitudes -30° and +20°. We generate synthetic photometric catalogs of complex stellar populations with different age and metallicity distributions, including the observational errors and completeness. The comparison between the color-magnitude diagrams of synthetic and observed disk-decontaminated bulge populations provides constraints on the stellar ages in the observed field. Results: We find the bulk of the bulge stellar population in the observed field along the minor axis to be older than ˜7.5 Gyr. In particular, when the metallicity distribution function spectroscopically derived by GIBS is used, the best fit to the data is obtained with a combination of synthetic populations with ages in between ˜7.5 Gyr and 11 Gyr. However, the fraction of stars younger than ˜10 Gyr strongly depends upon the number of blue straggler stars present in the bulge. Simulations show that the observed color-magnitude diagram of the bulge in the field along the minor axis is incompatible with the presence of a conspicuous population of intermediate-age and young (≲5 Gyr) stars. Based on observations taken within the ESO VISTA Public Survey VVV, Program ID 179.B-2002 (PI: Minniti, Lucas) and VIRCAM@VISTA/ESO, VVV, Program ID 095.B-0368(A) (PI: Valenti).