Resonant excitation of the biexciton state in an InAsP quantum dot by a phase-coherent pair of picosecond pulses allows for preparing time-bin entangled pairs of photons via the biexciton-exciton cascade. We show that this scheme can be efficiently implemented for a dot embedded in an InP nanowire. The underlying physical mechanisms can be represented and quantitatively analyzed by an effective three-level open system master equation. Simulation parameters including decay and intensity depending dephasing rates are extracted from experimental data, which in turn allow for predicting the resulting entanglement and finding optimal operating conditions.