We study the stellar populations of bulges of MilkyWay-like (MW-like) galaxies with the aim of identifying the physical processes involved in the formation of the bulge of our Galaxy. We use the semi-analytic model of galaxy formation and evolution SAG adapted to this aim; these kind of models can trace the properties of galaxies and their components like stellar discs, bulges and haloes, but resolution limits prevent them from reaching the scale of stellar populations (SPs). Properties of groups of stars formed during single star formation events are stored and tracked in the model and results are compared with observations of stars in the galactic bulge. MW-like galaxies are selected using two different criteria. One of them considers intrinsic photo-metric properties and the second is focused on the cosmological context of the local group (LG) of galaxies. We compare our model results with spectroscopic and photometric stellar metallicity distributions. We find that 87 per cent of stars in bulges of MW-type galaxies in our model are accreted and formed in starbursts during disc instability events. Mergers contribute to 13 per cent of the mass budget of the bulge and are responsible for the low metallicity tail of the distribution. Abundance ratios of α elements with respect to iron, [α/Fe], are measured in SPs of model galaxies. The patterns found in the model for SPs with different origins help to explain the lack of a gradient of [α/Fe] ratios in observed stars along the minor axis of the bulge.