The a<sup>137sup>Ba NMR and NQR spectra as well as the spin-lattice relaxation rate were measured for the first time in the BaPb<sub>xsub>Bi<sub>1−xsub>O<sub>3sub> samples with x = 0.91 (normal metal), x = 0.75 (superconductor) and x = 0.64 (semiconductor). The strong quadrupole broadening of the NMR lines with lowering temperature was found for all the samples. An evolution of static distortions in the BiO<sub>6sub>-octahedra sublattice along with asymmetry of the electric field gradient at the Ba-sites is discussed. This asymmetry caused by the nearest non-cubic surrounding of barium is originated from the temperature dependent tilt of BiO<sub>6sub>-octahedra. Spin-lattice relaxation rate of a<sup>137sup>Ba is monitored by fluctuating part of electric field gradient at the Ba-site and its exponential growth at low temperatures evidences the thermally activated collective rotations of BiO<sub>6sub>-octahedra around their static tilt. An activation energy and a strength of these dynamic distortions are evaluated and found to increase in going from metallic to semiconducting phase of BaPb<sub>xsub>Bi<sub>1−xsub>O<sub>3sub>.