Single-cycle interferometric autocorrelation measurements of electrons tunnelling across the gap of a plasmonic bowtie antenna and quantitative models provide insight into the physical interactions that drive the electron transfer. The strong fields associated with few-cycle pulses can drive highly nonlinear phenomena, allowing the direct control of electrons in condensed matter systems. In this context, by employing near-infrared single-cycle pulse pairs, we measure interferometric autocorrelations of the ultrafast currents induced by optical field emission at the nanogap of a single plasmonic nanocircuit. The dynamics of this ultrafast electron nanotransport depends on the precise temporal field profile of the optical driving pulse. Current autocorrelations are acquired with sub-femtosecond temporal resolution as a function of both pulse delay and absolute carrier-envelope phase. Quantitative modelling of the experiments enables us to monitor the spatiotemporal evolution of the electron density and currents induced in the system and to elucidate the physics underlying the electron transfer driven by strong optical fields in plasmonic gaps. Specifically, we clarify the interplay between the carrier-envelope phase of the driving pulse, plasmonic resonance and quiver motion.