We have performed a systematic study of the electronic structures of BiMeO3 (Me = Sc, Cr, Mn, Fe, Co, Ni) series by soft X-ray emission (XES) and absorption (XAS) spectroscopy. The band gap values were estimated for all compounds in the series. For BiFeO3 a band gap of ~0.9 eV was obtained from the alignment of the O Ka XES and O 1s XAS. The O 1s XAS spectrum of BiNiO3 indicates that the formation of holes is due to a Ni2+ valency rather than a Ni3+ valency. We have found that the O Ka XES and O 1s XAS of BiMeO3 probing partially occupied and vacant O 2p states, respectively, are in agreement with the O 2p densities of states obtained from spin-polarized band structure calculations. The O Ka XES spectra show the same degree of Bi 6s--O 2p hybridization for all compounds in the series. We argue herein that the stereochemical activity of Bi 6s lone pairs must be supplemented with inversion symmetry breaking to allow electric polarization. For BiMnO3 and BiFeO3, two cases of multiferroic materials in this series, the former breaks the inversion symmetry due to the antiferromagnetic order induced by particular orbital ordering in the highly distorted perovskite structure and the latter has rhombohedral crystal structure without inversion symmetry.