Several decades after the discovery of superconductivity in bismuthates, the strength of their electron-phonon coupling and its evolution with doping remain puzzling. To clarify these issues, polycrystalline hole-doped Ba_1−xK_xBiO₃ (0.1 ≤ x ≤ 0.6) samples were systematically synthesized and their bulk and microscopic superconducting properties were investigated by means of magnetic susceptibility and muon-spin rotation and relaxation (μSR), respectively. The phase diagram of Ba_1−xK_xBiO₃ was reliably extended up to x = 0.6, which is still found to be a bulk superconductor. The lattice parameter α increases linearly with K content, implying a homogeneous chemical doping. The low-temperature superfluid density, measured via transverse-field μSR, indicates an isotropic fully gapped superconducting state with zero-temperature gaps Δ₀/k_BT_c = 2.15, 2.10, and 1.75, and magnetic penetration depths λ₀ = 219, 184, and 279 nm for x = 0.3, 0.4, and 0.6, respectively. A change in the superconducting gap, from a nearly ideal BCS value (1.76k_BT_c in the weak-coupling case) in the overdoped x = 0.6 region, to much higher values in the optimally doped case, implies a gradual decrease in electron-phonon coupling with doping.