We propose a microscopic description of the bond-disproportionated insulating state in the bismuth perovskites XBiO3 (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 A1g symmetry composed of O-2pσ and Bi-6s atomic orbitals of collapsed BiO6 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.PACS numbers: 74.20. Pq,71.30.+h,71.45.Lr The physics of perovskite compounds, featuring BO 6 octahedra (B=cation) as building blocks, is exceptionally rich. The perovskites can be driven through a variety of structural, electronic, and magnetic phase transitions and are hosts to such intriguing states of matter as high-transition-temperature (T c ) superconductivity [cuprates [1], bismuth perovskites XBiO 3 (X=Ba, Sr) [2-4]], a pseudo-gap state with strongly violated Fermiliquid properties (cuprates[5]), and a spin/charge density wave [rare-earth nickelates RNiO 3 (R=rare-earth atom) [6]], to name a few. It is appealing to relate the diverse physical properties observed across the perovskite family of materials with the individual characteristics of the cation B. The latter can be magnetic (Cu in the cuprates) or not (Bi in the bismuth perovskites), orbitally active (Mn in the manganites [7]) or not (Cu, Bi), prone to strong electronic correlations (transition-metal elements Cu and Ni) or not (Bi). With the due appreciation of the cation factor, there are, however, many striking similarities among different perovskite families suggesting an equally important role of their common structural framework. A vivid example is the transition into a bond-disproportionated insulating phase found in both the bismuthates and the rare-earth nickelates, in which oxygen plays an extremely important role [8][9][10][11]. Observations of this kind have given rise to theories aimed at a unified description of the perovskites, where the various competing phases emerge from polaronic and bipolaronic excitations of the polarizable oxygen sublattice.While it is a common practice within this approach to assume that the only effect of electron-phonon coupling is variation of on-site energies, in this Letter we demonstrate that the effects due to hybridization between the oxygen-p orbitals and cation orbitals can be even more important. For this purpose, we focus on the bismuth perovskites XBiO 3 where the analysis is greatly facilitated by the fact that the Bi ion valence states are non-m...