  We study bottomonium production in association with an $\eta$ meson in
$e^+e^-$ annihilations near the $\Upsilon(5S)$, at a center of mass energy of
$\sqrt{s}=10.866\,$GeV. The results are based on the $121.4\,$fb$^{-1}$ data
sample collected by the Belle experiment at the asymmetric energy KEKB
collider. Only the $\eta$ meson is reconstructed and the missing-mass spectrum
of $\eta$ candidates is investigated. We observe the
$e^+e^-\to\eta\Upsilon_J(1D)$ process and find evidence for the
$e^+e^-\to\eta\Upsilon(2S)$ process, while no significant signals of
$\Upsilon(1S)$, $h_b(1P)$, nor $h_b(2P)$ are found. Cross sections for the
studied processes are reported.
