The response of a single InGaAs quantum dot, embedded in a miniaturized charge-tunable device, to an applied GHz bandwidth electrical pulse is investigated via its optical response. Quantum-dot response times of 1.0 +/- 0.1 ns are characterized via several different measurement techniques, demonstrating GHz-bandwidth electrical control. Furthermore, a novel optical detection technique based on resonant electron-hole pair generation in the hybridization region is used to map fully the voltage pulse experienced by the quantum dot, showing, in this case, a simple exponential rise.