How do Gram + bacteria use a proton gradient for F-type ATPase?
Protons are pumped out of the bacterial cell by the electron tansport chain. This creates a protonmotive force with two components, one due to the difference in proton concentration, the other due to the membrane potential that is created. In bacteria and mitochondria it is the membrane potential component that provides most of the driving force to pull protons back in through the ATP synthase. Thus the fate of the protons outside the cell doesn't matter too much. Even if you were to buffer the exterior absolutely, the fact that charge had moved out would drive ATP synthesis.