The effect of structural relaxation on electrical resistivity, ρ, of strain-free ZrTiCuNiBe bulk metallic glass was studied during isothermal aging at several temperatures, Ts. Since cooling of a liquid metal increases its resistivity ρ, one expects ρ to increase on aging toward ρ at T = T. Instead, ρ decreased non-exponentially with the aging time. The activation energy of aging kinetics is 189 kJ mol, which is higher than the activation energy of the Johari-Goldstein (JG) relaxation. After considering the sample's contraction, phase separation, and crystallization as possible causes of the decrease in ρ, we attribute the decrease to depletion of islands of atomic mobility, soft spots, or static heterogeneity. Vibrations of the atoms in these local (loosely packed) regions and in the region's interfacial area contribute to electron scattering. As these deplete on aging, the contribution decreases and ρ decreases, with a concomitant decrease in macroscopic volume, enthalpy, and entropy (V, H, and S). Local regions of faster mobility also decrease on cooling as V, H, and S of a liquid decrease, but structure fluctuations dominate electron scattering of a liquid metal and ρ increases effectively according to the Ziman-Nagel theory for a homogenously disordered structure. Whether depletion of such local regions initiates the structural relaxation of a glass, or vice versa, may be resolved by finding a glass that physically ages but shows no JG relaxation.