Ba_1-xK_xBiO₃ (BKBO) has long been a subject of great interest due to its intertwined electronic and structural properties. Recently, comparative material Ba_1-xK_xSbO₃ (BKSO) is also successfully synthesized and exhibits a similar phase diagram with BKBO. It is well established that the simple DFT fails to describe several physical properties of BKBO compound while the hybrid functional or GW methods are better in many aspects although comprehensive studies for its entire phase diagram are limited due to their expensive computational cost. Here, based on a newly developed ab initio method counting self-consistent on- and inter-site Coulomb interactions, we examine the electronic, structural, and phonon properties of BKBO and BKSO with various potassium doping levels. Our new method can describe the bandgaps and phonon dispersions of semiconductors precisely in a similar level to the GW method, but at the simple DFT computational cost. We found that the new method gives much improved results compared to the simple DFT calculations. A comprehensive comparative study on the electronic and structural properties of BKBO and BKSO will be discussed.