ABSTRACT Active galactic nucleus (AGN) growth in disc-dominated, merger-free galaxies is poorly understood, largely due to the difficulty in disentangling the AGN emission from that of the host galaxy. By carefully separating this emission, we examine the differences between AGNs in galaxies hosting a (possibly) merger-grown, classical bulge, and AGNs in secularly grown, truly bulgeless disc galaxies. We use galfit to obtain robust, accurate morphologies of 100 disc-dominated galaxies imaged with the Hubble Space Telescope. Adopting an inclusive definition of classical bulges, we detect a classical bulge component in $53.3 \pm 0.5$ per cent of the galaxies. These bulges were not visible in Sloan Digital Sky Survey photometry, however these galaxies are still unambiguously disc-dominated, with an average bulge-to-total luminosity ratio of $0.1 \pm 0.1$. We find some correlation between bulge mass and black hole mass for disc-dominated galaxies, though this correlation is significantly weaker in comparison to the relation for bulge-dominated or elliptical galaxies. Furthermore, a significant fraction ($\gtrsim 90$ per cent) of our black holes are overly massive when compared to the relationship for elliptical galaxies. We find a weak correlation between total stellar mass and black hole mass for the disc-dominated galaxies, hinting that the stochasticity of black hole–galaxy co-evolution may be higher in disc-dominated than bulge-dominated systems.