  The $R$-parity violating decays of Bino neutralino LSPs are analyzed within
the context of the $B-L$ MSSM "heterotic standard model". These LSPs correspond
to statistically determined initial soft supersymmetry breaking parameters
which, when evolved using the renormalization group equations, lead to an
effective theory satisfying all phenomenological requirements; including the
observed electroweak vector boson masses and the Higgs mass. The explicit RPV
decay channels of these LSPs into standard model particles, the analytic and
numerical decay rates and the associated branching ratios are presented. The
analysis of these quantities breaks into two separate calculations; first, for
Bino neutralino LSPs with mass larger than $M_{W^{\pm}}$ and, second, when the
Bino neutralino mass is smaller than the electroweak scale. The RPV decay
processes in both of these regions is analyzed in detail. The decay lengths of
these RPV interactions are discussed. It is shown that for heavy Bino
neutralino LSPs the vast majority of these decays are "prompt", although a
small, but calculable, number correspond to "displaced" decays of various
lengths. The situation is reversed for light Bino LSPs, only a small number of
which can RPV decay promptly. The relation of these results to the neutrino
hierarchy--either normal or inverted--is discussed in detail.
