In this paper we investigate a concentration-dependent Schmidt number description and two near-bed boundary conditions, empirical pickup and reference concentration, for a dilute two-phase sediment transport model with a k-$varepsilon$ fluid turbulence closure. The pick-up approach adopts an empirical formula to calculate the upward sediment flux, whereas the reference concentration approach relates the upward sediment flux to the concentration at a reference location above the initially undisturbed bed. Through model-data comparisons with data measured in the U tube, we show that the variation of Schmidt number only affects the magnitude of calculated concentration and is insensitive to the predicted phase of concentration time histories. The predicted phase is found more sensitive to the near-bed sediment boundary condition. A concentration-dependent Schmidt number is then introduced, which improves the predictions of magnitude and phase of concentration. Using the concentration-dependent Schmidt number, the reference concentration approach generally predicts suspended sediment concentration better than the pick-up approach does.