  The dipion transitions $\Upsilon(2S,3S,4S) \to \Upsilon(1S,2S)\pi\pi$ are
systematically studied by considering the mechanisms of the hadronization of
soft gluons, exchanging the bottomoniumlike $Z_b$ states, and the bottom-meson
loops. The strong pion-pion final-state interaction, especially including the
channel coupling to $K\bar{K}$ in the $S$-wave, is taken into account in a
model-independent way using the dispersion theory. Through fitting to the
available experimental data, we extract values of the transition
chromopolarizabilities $|\alpha_{\Upsilon(mS)\Upsilon(nS)}|$, which measure the
chromoelectric couplings of the bottomonia with soft gluons. It is found that
the $Z_b$ exchange has a slight impact on the extracted chromopolarizablity
values, and the obtained $|\alpha_{\Upsilon(2S)\Upsilon(1S)}|$ considering the
$Z_b$ exchange is $(0.29\pm 0.20)~\text{GeV}^{-3}$. Our results could be useful
in studying the interactions of bottomonium with light hadrons.
