  We estimate the branching ratio for the inclusive decays $\Xi_{bbq}
\rightarrow {\bar B}_c^{(*)}+X_{c,s,q}$ to be approximately 1%. Our estimate is
performed using non-relativistic potential quark model methods that are
appropriate if the bottom and charm quarks are heavy compared to the strong
interaction scale. Here the superscript $(*)$ denotes that we are summing over
spin zero ${\bar B}_c$ and spin one ${\bar B}_c^*$ mesons and the subscript $q$
denotes a light quark. Our approach treats the two bottom quarks in the baryon
$\Xi_{bbq}$ as a small color anti-triplet. This estimate for the inclusive
branching ratio to ${\bar B}_c$ and ${\bar B}^*_c$ mesons also holds for decays
of the lowest lying $T_{bb{\bar q}{\bar q}}$ tetraquark states, provided they
are stable against strong and electromagnetic decay.
