The central black hole masses of a sample of 30 luminous quasars are estimated using Hβ full width half-maximum (FWHM) measurements from a combination of new and previously published nuclear spectra. The quasar black hole mass estimates are combined with reverberation-mapping measurements for a sample of Seyfert galaxies in order to study active galatic nucleus (AGN) black hole masses over a wide range in nuclear luminosity. The link between bulge luminosity and black hole mass is investigated using two-dimensional disc/bulge decompositions of the host galaxy images, the vast majority of which are high-resolution Hubble Space Telescope (HST) observations. It is found that black hole mass and bulge luminosity are well correlated and follow a relation consistent with that expected if black hole and bulge mass are directly proportional. Contrary to the recent results of Wandel, no evidence that Seyfert galaxies follow a different Mbh-Mbulge relation to quasars is found. However, the black hole mass distributions of the radio-loud and radio-quiet quasar subsamples are found to be significantly different, with the median black hole mass of the radio-loud quasars a factor of three larger than their radio-quiet counterparts. Finally, utilizing the elliptical galaxy fundamental plane to provide stellar velocity dispersion estimates, a comparison is performed between the virial Hβ black hole mass estimates and those of the Mbh-σ correlations of Gebhardt et al. and Merritt & Ferrarese. With the disc geometry of the broad-line region adopted in this paper, the virial Hβ black hole masses indicate that the correct normalization of the black hole versus bulge mass relation is Mbh~=0.0025Mbulge, while the standard assumption of purely random broad-line velocities leads to Mbh~=0.0008Mbulge. The normalization of Mbh~=0.0025Mbulge provided by the disc model is in remarkably good agreement with that inferred for our quasar sample using the (completely independent) Mbh-σ correlations.