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Despite much effort, the local structure of the high-T_c superconductor Ba_1-xK_xBiO₃ remains poorly understood. Here we present extensive diffuse x-ray scattering measurements on single crystal of Ba_1-xK_xBiO₃, with data on either side of the semiconductor-metal transition at x ~ 0.35. Bismuth valence disproportionation that leads to a breathing distortion of the oxygen octahedra and causes a charge-density wave provides a good explanation for the structure of the undoped material. However, the 3D-pair distribution function (3D-ΔPDF) obtained from our diffuse x-ray scattering data indicates that this picture may not be appropriate for the doped system. The oxygen octahedra in ABiO₃ perovskites are known to tilt in order to accommodate atoms on the A site. Our 3D-ΔPDF and accompanying Monte Carlo modeling work indicates that various tilt modes are prominent in the metallic regime, along with substantial size-effect distortions caused by potassium doping. These lattice deformations lead to a lowered local symmetry, with profound implications for both the normal and superconducting states.