We present the radial profiles of the Hβ, Mg and Fe line‐strength indices for a sample of eight spiral galaxies with a low‐surface‐brightness stellar disc and a bulge. The correlations between the central values of the line‐strength indices and velocity dispersion are consistent with those known for early‐type galaxies and bulges of high‐surface‐brightness galaxies. The age, metallicity and α/Fe enhancement of the stellar populations in the bulge‐dominated region are obtained using stellar population models with variable element abundance ratios. Almost all the sample bulges are characterized by a young stellar population, ongoing star formation and a solar α/Fe enhancement. Their metallicity spans from high to subsolar values. No significant gradient in age and α/Fe enhancement is measured, whereas a negative metallicity gradient is found only in a few cases. These properties suggest that a pure dissipative collapse cannot explain the formation of all the sample bulges and that other phenomena, such as mergers or acquisition events, need to be invoked. Such a picture is also supported by the lack of a correlation between the central value and the gradient of the metallicity in bulges with very low metallicity. The stellar populations of the bulges hosted by low‐surface‐brightness discs share many properties with those of high‐surface‐brightness galaxies. Therefore, they are likely to have common formation scenarios and evolution histories. A strong interplay between bulges and discs is ruled out by the fact that, in spite of being hosted by discs with extremely different properties, the bulges of low‐ and high‐surface‐brightness discs are remarkably similar.