  In this work, we investigate the hadronic loop contributions to the
$\Upsilon(6S) \to \chi_{bJ} \phi~(J=0,1,2)$ along with $\Upsilon(6S) \to
\chi_{bJ} \omega~(J=0,1,2)$ transitions. We predict that the branching ratios
of $\Upsilon(6S) \to \chi_{b0} \phi$, $\Upsilon(6S) \to \chi_{b1} \phi$ and
$\Upsilon(6S) \to \chi_{b2} \phi$ are $(0.68 \sim 4.62) \times 10^{-6}$, $(0.50
\sim 3.43) \times 10^{-6}$ and $(2.22 \sim 15.18) \times 10^{-6}$, respectively
and those of $\Upsilon(6S) \to \chi_{b0} \omega$, $\Upsilon(6S) \to \chi_{b1}
\omega$ and $\Upsilon(6S) \to \chi_{b2} \omega$ are $(0.15 \sim 2.81) \times
10^{-3}$, $(0.63 \sim 11.68) \times 10^{-3}$ and $(1.08 \sim 20.02) \times
10^{-3}$, respectively. Especially, some typical ratios, which reflect the
relative magnitudes of the predicted branching ratios, are given, i.e., for
$\Upsilon(6S)\to \chi_{bJ}\phi$ transitions,
$\mathcal{R}^\phi_{10}={\mathcal{B}[\Upsilon(6S) \to \chi_{b1}
\phi]}/{\mathcal{B}[\Upsilon(6S) \to \chi_{b0} \phi]} \approx 0.74$,
$\mathcal{R}^\phi_{20}= {\mathcal{B}[\Upsilon(6S) \to \chi_{b2}
\phi]}/{\mathcal{B}[\Upsilon(6S) \to \chi_{b0} \phi]} \approx 3.28$, and
$\mathcal{R}^\phi_{21} = {\mathcal{B}[\Upsilon(6S) \to \chi_{b2}
\phi]}/{\mathcal{B}[\Upsilon(6S) \to \chi_{b1} \phi]} \approx 4.43$, and for
$\Upsilon(6S)\to \chi_{bJ}\omega$ transitions,
$\mathcal{R}^\omega_{10}={\mathcal{B}[\Upsilon(6S) \to \chi_{b1}
\omega]}/{\mathcal{B}[\Upsilon(6S) \to \chi_{b0} \omega]} \approx 4.11$,
$\mathcal{R}^\omega_{20}= {\mathcal{B}[\Upsilon(6S) \to \chi_{b2}
\omega]}/{\mathcal{B}[\Upsilon(6S) \to \chi_{b0} \omega]} \approx 7.06$, and
$\mathcal{R}^\omega_{21} = {\mathcal{B}[\Upsilon(6S) \to \chi_{b2}
\omega]}/{\mathcal{B}[\Upsilon(6S) \to \chi_{b1} \omega]} \approx 1.72$. With
the running of BelleII in the near future, experimental measurement of these
two kinds of transitions will be a potential research issue.
