  We study the decays $\bar B^0 \to \bar K^0 \, X$, $B^- \to K^- \, X$, $\bar
B^0_s \to \eta (\eta')\, X$, $\bar B^0 \to \bar K^{*0} \, X$, $B^- \to K^{*-}
\, X$ , $\bar B_s^0 \to \phi \, X$, with $X \equiv X(3872)$, from the
perspective of the $X(3872)$ being a molecular state made from the interaction
of the $D^{*+} D^-, D^{*0} \bar D^0$ and $c.c.$ components. We consider both
the external and internal emission decay mechanisms and find an explanation for
the $\bar K^0 \, X$ and $K^- \, X$ production rates, based on the mass
difference of the charged and neutral $D^* \bar D$ components. We also find
that the internal and external emission mechanisms add constructively in the
$\bar B^0 \to \bar K^0 \, X$, $B^- \to K^- \, X$ reactions, while they add
destructively in the case of $\bar B^0 \to \bar K^{*0} \, X$, $B^- \to K^{*-}
\, X$ reactions. This feature explains the decay widths of the present
measurements and allows us to make predictions for the unmeasured modes of
$\bar B^0_s \to \eta (\eta')\, X(3872)$ and $B^- \to K^{*-} \, X(3872)$. The
future measurement of these decay modes will help us get a better perspective
on the nature of the $X(3872)$ and the mechanisms present in production
reactions of that state.
