  We propose a microscopic description of the bond-disproportionated insulating
state in the bismuth perovskites $X$BiO$_3$ ($X$=Ba, Sr) that recognizes the
bismuth-oxygen hybridization as a dominant energy scale. It is demonstrated
using electronic structure methods that the breathing distortion is accompanied
by spatial condensation of hole pairs into local, molecular-like orbitals of
the $A_{1g}$ symmetry composed of O-$2p_{\sigma}$ and Bi-$6s$ atomic orbitals
of collapsed BiO$_6$ octahedra. Primary importance of oxygen $p$-states is thus
revealed, in contrast to a popular picture of a purely ionic
Bi$^{3+}$/Bi$^{5+}$ charge-disproportionation. Octahedra tilting is shown to
enhance the breathing instability by means of a non-uniform band-narrowing. We
argue that formation of localized states upon breathing distortion is, to a
large extent, a property of the oxygen sublattice and expect similar
hybridization effects in other perovskites involving formally high oxidation
state cations.
