We use simulations to study the growth of a pseudobulge in an isolated thin exponential stellar disc embedded in a static spherical halo. We observe a transition from later to earlier morphological types and an increase in bar prominence for higher disc-to-halo mass ratios, for lower disc-to-halo size ratios, and for lower halo concentrations. We compute bulge-to-total stellar mass ratios B/T by fitting a two-component Sérsic-exponential surface-density distribution. The final B/T is strongly related to the disc’s fractional contribution fd to the total gravitational acceleration at the optical radius. The formula B/T = 0.5 fd1.8 fits the simulations to an accuracy of 30%, is consistent with observational measurements of B/T and fd as a function of luminosity, and reproduces the observed relation between B/T and stellar mass when incorporated into the GALICS 2.0 semi-analytic model of galaxy formation.