In the cubic, stoichiometric oxide compounds Bi2Ti2O6O′ (also written as Bi2Ti2O7) and Bi2Ru2O6O′ (also written as Bi2Ru2O7) Bi3+ ions on the pyrochlore A site display a propensity to off-center. Unlike Bi2Ti2O6O′, Bi2Ru2O6O′ is a metal, so it is of interest to ask whether conduction electrons and/or involvement of Bi 6s states at the Fermi energy influence Bi3+ displacements. The Bi3+ off-centering in Bi2Ti2O6O′ has previously been revealed to be incoherent from detailed reverse Monte Carlo analysis of total neutron scattering. Similar analysis of Bi2Ru2O6O′ reveals incoherent off-centering as well, but of smaller magnitude and with distinctly different orientational preference. Analysis of the distributions of metal to oxygen distances presented suggests that Bi in both compounds is entirely Bi3+. Disorder in Bi2Ti2O6O′ has the effect of stabilizing valence while simultaneously satisfying the steric constraint imposed by the presence of the lone pair of electrons. In Bi2Ru2O6O′, off-centering is not required to satisfy valence and seems to be driven by the lone pair. Decreased volume of the lone pair may be a result of partial screening by conduction electrons.