The saturation behavior of the nonlinear index delta-n(NL) in the band tail of GaAs/AlGaAs multiple quantum wells is experimentally studied in quasi-steady state and in a low absorption region (below 300 cm-1), where dispersive optical bistability is observed. Measurements at different detunings from the exciton resonance allow us to study the absorption dependence of the saturation parameters. The saturation intensity I(S) is found inversely proportional to the linear absorption coefficient, while the saturating nonlinear index delta-n(S) is approximately constant. This evidences that the nonlinear index saturation is due to a saturation of the carrier density versus light intensity, due to the saturation of the band tail absorption itself.