There are diverse interdisciplinary applications for nanoscale-resolution electrometry of elementary charges under ambient conditions. These include characterization of two-dimensional electronics, charge transfer in biological systems, and measurement of fundamental physical phenomena. The nitrogen-vacancy center in diamond is uniquely capable of such measurements, however electrometry thus far has been limited to charges within the same diamond lattice. It has been hypothesized that the failure to detect charges external to diamond is due to quenching and surface screening, but no proof, model, or design to overcome this has yet been proposed. In this work we affirm this hypothesis through a comprehensive theoretical model of screening and quenching within a diamond electrometer and propose a solution using controlled nitrogen doping and a fluorine-terminated surface. We conclude that successful implementation requires further work to engineer diamond surfaces with lower surface-defect concentrations.