ABSTRACT Due to its proximity, the stellar populations of the Galactic bulge (GB) can be resolved and can be studied in detail. This allows tracing the bulge metallicity distribution function (MDF) for different spatial regions within the bulge, which may give us clues about the bulge formation and evolution scenarios. In this work, we developed a chemical evolution model (CEM), taking into account the mass distribution in the bulge and disc, to derive the radial dependence of this time-scale in the Galaxy. Since the infall rate depends on that time-scale in the CEM, the results of the model were used to test a scenario where the bulge is formed inside-out. The obtained results for the α/Fe versus Fe/H relationship, the MDF and the Fe/H radial gradient in the bulge have been compared to available data in the literature. The model is able to reproduce most of the observational data: the spread in the relation α/Fe versus Fe/H, the MDF shape in different regions of the bulge, the Fe/H radial gradient inside it, and the age–metallicity relation, as well as the α/Fe evolution with age. The results of the model point to a scenario where the bulk of the bulge stars pre-existed the boxy/peanut X-shape bar formation. As a result, the classical origin of the GB is not ruled out, and this scenario may be invoked to explain the chemical properties of the GB.