The long time response of a bistable stochastic model driven by large amplitude time-dependent sinusoidal fields is investigated by numerically solving the Langevin or the Fokker-Planck equation. The noise average behavior is oscillatory in time. For a given strength of the driving field, the behavior with the noise of the amplitude and phase of the fundamental harmonics of the average response depends on the frequency. For large driving frequencies, both magnitudes show maxima for two different values of the noise intensity. For a small enough external frequency, those maxima are absent.