Bipolaronic superconductivity is an exotic pairing mechanism proposed for materials like BKBO; however, conclusive experimental evidence for a (bi)polaron metallic state in this material remains elusive. Here, we combine resonant inelastic x-ray and neutron total scattering techniques with advanced modelling to study the local lattice distortions, electronic structure, and e-ph coupling in BKBO as a function of doping. Data for the parent compound (x = 0) indicates that the electronic gap opens in predominantly oxygen-derived states strongly coupled to a long-range ordered breathing distortion of the oxygen sublattice. Upon doping, short-range breathing distortions and sizable e-ph coupling persist into the superconducting regime (x = 0.4). Comparisons with exact diagonalization and determinant quantum Monte Carlo calculations further support this conclusion. Our results provide compelling evidence that BKBO's metallic phase hosts a liquid of small (bi)polarons derived from local breathing distortions of the lattice, with implications for understanding the low-temperature superconducting instability.