A comprehensive assessment of the nature of the distribution of sub band-gap energy states in bulk GaAsBi is presented using power and temperature dependent photoluminescence spectroscopy. The observation of a characteristic red-blue-red shift in the peak luminescence energy indicates the presence of short-range alloy disorder in the material. A decrease in the carrier localisation energy demonstrates the strong excitation power dependence of localised state behaviour and is attributed to the filling of energy states furthest from the valence band edge. Analysis of the photoluminescence lineshape at low temperature presents strong evidence for a Gaussian distribution of localised states that extends from the valence band edge. Furthermore, a rate model is employed to understand the non-uniform thermal quenching of the photoluminescence and indicates the presence of two Gaussian-like distributions making up the density of localised states. These components are attributed to the presence of microscopic fluctuations in Bi content, due to short-range alloy disorder across the GaAsBi layer, and the formation of Bi related point defects, resulting from low temperature growth.