  Bismuth perovskites ABiO$_3$ (A = Sr, Ba) host a variety of peculiar
phenomena including bond-disproportionated insulating phases and
high-temperature superconductivity upon hole doping. While the mechanisms
underlying these phenomena are still debated, off-diagonal electron-phonon
($e$-ph) coupling originating from the modulation of the orbital overlaps has
emerged as a promising candidate. Here, we employ classical Monte Carlo
simulations to study a semiclassical three-orbital model with off-diagonal
$e$-ph interactions. We demonstrate the existence of a (bi)polaron correlations
that persists in the model at high temperatures and for hole doping away from
the bond-disproportionated insulating phase. Using a spatiotemporal regression
analysis between various local quantities and the lattice degrees of freedom,
we also identify the similarity between heating- and doping-induced melting of
a bond-disproportionated insulator at a microscopic level. Our results imply
that (bi)polaron physics can be a unifying concept that helps us understand the
rich bismuth perovskite phase diagram.
