Electrochemical gradients established across biological membranes are fundamental in the bioenergetics of all forms of life. In bacteria, the proton motive force (PMF), the electrochemical potential associated to protons, powers an impressive array of fundamental processes, from ATP production to motility. While far from equilibrium, it has classically been considered homeostatic in time and space. Yet, recent experiments have revealed rich temporal dynamics at the single cell level and functional spatial dynamics at the scale of multicellular communities. Lateral segregation of supramolecular respiratory complexes begs the question of whether spatial heterogeneity of the PMF exists even at the single cell level. By using a light-activated proton pump as a spatially and temporally modulatable source, and the bacterial flagellar motor as a local electro-mechanical gauge, we both perturb and probe the PMF on single cells. Using global perturbations, we resolve temporal dynamics on the ms time scale and observe an asymmetrical capacitive response of the cell. Using localized perturbations, we find that the PMF is rapidly homogenized along the entire cell, faster than proton diffusion can allow. Instead, the electrical response can be explained in terms of electrotonic potential spread, as found in passive neurons and described by cable theory. This implies a global coupling between PMF sources and consumers in the bacterial membrane, excluding a sustained spatial heterogeneity while allowing for fast temporal dynamics.