The bistable nonlinear energy sink (NES) shows high efficiency in mitigating vibration through targeted energy transfer (TET). It performs well in low- and high-energy input cases, whereas, for a cubic NES, TET occurs only above a certain energy threshold. In this work, the measure of energy pumping time is extended to a harmonic excitation case by the application of a particular integration assumption. An equivalent point in the slow invariant manifold (SIM) structure can represent the average variation of the amplitudes of linear oscillator (LO) and NES. The marked robustness of this semi-analytical prediction method under parameter perturbation is investigated numerically here. The influence of parameters on the rate at which the amplitude declines is also investigated for both impulsive and harmonic excitation. The pumping time estimation is validated in a low-energy input experimental test.