  We consider the embedding of the supersymmetric Standard Model with broken
R-parity in the minimal supergravity (mSUGRA) model. We restrict ourselves to
the case of broken lepton number, the B3 mSUGRA model. We first study in detail
how the tree-level neutrino mass depends on the mSUGRA parameters. We find in
particular a strong dependence on the trilinear supersymmetry breaking
A-parameter, even in the vicinity of the mSUGRA SPS1a point. We then
reinvestigate the bounds on the trilinear R-parity violating couplings at the
unification scale from the low-energy neutrino masses including dominant
one-loop contributions. These bounds were previously shown to be very strict,
as low as O(10^{-6}) for SPS1a. We show that these bounds are significantly
weakened when considering the full mSUGRA parameter space. In particular the
ratio between the tree-level and 1-loop neutrino masses is reduced such that it
may agree with the observed neutrino mass hierarchy. We discuss in detail how
and in which parameter regions this effect arises.
