  Using data collected with the Belle detector at the KEKB asymmetric-energy
$e^+e^-$ collider, we measure the energy dependence of the $e^+e^- \to
h_b(nP)\pi^+\pi^-$ $(n=1,2)$ cross sections from thresholds up to $11.02\,$GeV.
We find clear $\Upsilon(10860)$ and $\Upsilon(11020)$ peaks with little or no
continuum contribution. We study the resonant substructure of the
$\Upsilon(11020) \to h_b(nP)\pi^+\pi^-$ transitions and find evidence that they
proceed entirely via the intermediate isovector states $Z_b(10610)$ and
$Z_b(10650)$. The relative fraction of these states is loosely constrained by
the current data: the hypothesis that only $Z_b(10610)$ is produced is excluded
at the level of 3.3 standard deviations, while the hypothesis that only
$Z_b(10650)$ is produced is not excluded at a significant level.
