  The fraction of $J/\psi$ mesons which come from B-meson decay,
$\textrm{F}_{B{\rightarrow}J/\psi}$, is measured for J/$\psi$ rapidity
\mbox{$1.2<|y|<2.2$} and $p_T>0$ in $p$+$p$ and Cu+Au collisions at
$\sqrt{s_{_{NN}}}$=200 GeV with the PHENIX detector. The extracted fraction is
$\textrm{F}_{B{\rightarrow}J/\psi}$ = 0.025 $\pm$ 0.006(stat) $\pm$ 0.010(syst)
for $p$+$p$ collisions. For Cu+Au collisions,
$\textrm{F}_{B{\rightarrow}J/\psi}$ is 0.094 $\pm$ 0.028(stat) $\pm$
0.037(syst) in the Au-going direction ($-2.2<y<-1.2$) and 0.089 $\pm$
0.026(stat) $\pm$ 0.040(syst) in the Cu-going direction ($1.2<y<2.2$). The
nuclear modification factor, $R_{\rm CuAu}$, of B mesons in Cu+Au collisions is
consistent with binary scaling of measured yields in $p$+$p$ at both forward
and backward rapidity.
