We investigate the electronic conductance and thermopower of a single-molecule junction consisting of bis-(4-aminophenyl) acetylene (B4APA) connected to gold electrodes. We use nonequilibrium Green's function methods in combination with density-functional theory (DFT) and the many-body GW approximation. To simulate recent break junction experiments, we calculate the transport properties of the junction as it is pulled apart. For all junction configurations, DFT with a standard semilocal functional overestimates the conductance by almost an order of magnitude, while the thermopower is underestimated by up to a factor of 3, except for the most highly stretched junction configurations. In contrast, the GW results for both conductance and thermopower are in excellent agreement with experiments for a wide range of electrode separations. We show that the GW self-energy not only renormalizes the molecular energy levels but also the coupling strength. The latter is a consequence of the finite response time associated with the electronic screening in the metal electrodes.