  Several independent lines of evidence now point to a correlation between
black hole mass, M_bh, and radio-luminosity. In this paper we discuss the
correlation for quasars from the FIRST Bright Quasar Survey (FBQS), using black
hole mass estimates from Hbeta linewidths. The FBQS objects fill in the gap
between the radio-loud and radio-quiet quasars in the radio-luminosity -
optical-luminosity plane, and we find that they fill the corresponding gap in
the M_bh - radio luminosity correlation. There is thus a continuous variation
of radio luminosity with M_bh, and no evidence for a ``switch'' at some set of
critical parameter values which turns on powerful radio jets. By combining the
FBQS data with that for quasars from the Palomar-Green survey we find evidence
for a dependence of radio-luminosity on accretion rate relative to the
Eddington limit, L/L_Edd, as well as on M_bh, consistent with the well-known
radio-optical correlation for radio-loud quasars. We therefore suggest a new
scheme to ``unify'' radio-loud and radio-quiet objects in which radio
luminosity scales proportional to M_bh^{1.9+/-0.2}(L/L_Edd)^{1.0} for
L/L_Edd~0.1, with an apparently weaker accretion rate dependence at low
L/L_Edd. The scatter about this relation is +/-1.1 dex, and may well hide
significant contributions from other physical effects, such as black hole spin
and radio source environment.
