A new method is described to obtain the drift mobility of band-tail carriers in doped hydrogenated amorphous silicon from dc-conductivity and sweep-out measurements. Analysis finds that above room temperature, the drift mobility in n-type samples is independent of the density of carriers and depends only on the density-of-states distribution, the position of the mobility edge, and the free-carrier mobility. Experiments confirm the analysis and show that the drift mobility decreases by about an order of magnitude with n-type doping. Numerical modeling of the transport indicates that the reduction in mobility is primarily due to an apparent upward shift of the mobility edge. The transport mechanisms, and the relation between the measured drift mobility and thermoelectric-power data, are discussed in terms of long-range potential fluctuations arising from charged electronic states.