Narrow bipolar pulses (NBPs) are a class of high-altitude, high-energy discharges that occur during some thunderstorms. We use a modified transmission line model (called MTLEI) with a current that increases exponentially along the propagation channel to test mechanisms that might produce NBPs. Model outputs were compared to measured E data from a single NBP collected at near and far field locations. We were unable to fit the measured data using the fast current propagation speeds appropriate for a runaway breakdown/extensive air shower mechanism. Instead, by using currents that travel relatively slowly (6 W 107 m/s), the MTLEI model fit the data reasonably well. This result is compatible with a mechanism that uses runaway breakdown to produce charge carriers along with a moving electric field to drive the main NBP current. Using this model for the measured NBP, we estimate a charge moment of 0.6 C7km.