Using time-resolved photoluminescence spectroscopy, we explore the transient behavior of bound and free excitons in GaN nanowire ensembles. We investigate samples with distinct diameter distributions and show that the pronounced biexponential decay of the donor-bound exciton observed in each case is not caused by the nanowire surface. At long times, the individual exciton transitions decay with a common lifetime, which suggests a strong coupling between the corresponding exciton states. A system of nonlinear rate equations taking into account this coupling directly reproduces the experimentally observed biexponential decay.