We use quasi-simultaneous near-infrared (near-IR) and optical spectroscopy from four observing runs to study the continuum around 1 micron in 23 well-known broad-emission line active galactic nuclei (AGN). We show that, after correcting the optical spectra for host galaxy light, the AGN continuum around this wavelength can be approximated by the sum of mainly two emission components, a hot dust blackbody and an accretion disc. The accretion disc spectrum appears to dominate the flux at ~1 micron, which allows us to derive a relation for estimating AGN black hole masses based on the near-IR virial product. This result also means that a near-IR reverberation programme can determine the AGN state independent of simultaneous optical spectroscopy. On average we derive hot dust blackbody temperatures of ~1400 K, a value close to the sublimation temperature of silicate dust grains, and relatively low hot dust covering factors of ~7%. Our preliminary variability studies indicate that in most sources the hot dust emission responds to changes in the accretion disc flux with the expected time lag, however, a few sources show a behaviour that can be attributed to dust destruction.