The carrier dynamics of a Ga(AsBi)/GaAs single quantum well (SQW) with a Bi content of 5.5% are studied by means of time-resolved photoluminescence (PL). Random fluctuation of the alloy compositions and the presence of Bi clusters in the QW material, lead to localized states and have a significant influence on the mechanism of the PL emission. Under low excitation conditions, the PL emission is dominated by the recombination of localized electron-hole pairs. The PL spectra exhibit a considerable blue-shift with increased excitation intensity due to the filling of localized states. At high excitation intensities, additional PL signatures at the high energy side of the main emission peak evolve, corresponding to higher confined states of the quantum well. Also, the role of the carrier hopping between localized states becomes smaller. In addition, a shortening of the PL decay time is observed at increased lattice temperatures due to the delocalization of carriers, leading to faster non-radiative recombination. The latter is accompanied by the quenching of the PL intensity.