We seek to understand whether the stellar populations of galactic bulges show evidence of secular evolution triggered by the presence of the disc. For this purpose we re-analyse the sample of Proctor and Sansom, deriving stellar population ages and element abundances from absorption line indices as functions of central velocity dispersion and Hubble type. We obtain consistent constraints on ages from the three Balmer line indices Hβ, Hγ, and Hδ, based on stellar population models that take the abundance ratio effects on these indices into account. Emission line contamination turns out to be a critical aspect, which favours the use of the higher-order Balmer line indices. Our derived ages are consistent with those of Proctor and Sansom based on a completely different method. In agreement with other studies in the literature, we find that bulges have relatively low luminosity weighted ages, the lowest age derived being 1.3 Gyr. Hence bulges are not generally old, but actually rejuvenated systems. We discuss evidence that this might be true also for the bulge of the Milky Way. The data reveal clear correlations of all three parameters luminosity weighted age, total metallicity, and α/Fe ratio with central velocity dispersion. The smallest bulges are the youngest with the lowest α/Fe ratios owing to late Fe enrichment from Type Ia supernovae. Using models combining recent minor star formation with a base old population, we show that the smallest bulges must have experienced significant star formation events involving 10 − 30 per cent of their total mass in the past 1 − 2 Gyr. No significant correlations of the stellar population parameters with Hubble Type are found. We show that the above relationships with σ coincide perfectly with those of early-type galaxies. In other words, bulges are typically younger, metal-poorer and less α/Fe enhanced than early-type galaxies, because of their smaller masses. At a given velocity dispersion, bulges and elliptical galaxies are indistinguishable as far as their stellar populations are concerned. These results favour an inside-out formation scenario and indicate that the discs in spiral galaxies of Hubble types Sbc and earlier cannot have a significant influence on the evolution of the stellar populations in the bulge component. The phenomenon of pseudobulge formation must be restricted to spirals of types later than Sbc.