In this paper we are concerned with the efficiency and robustness of different optimal pulses that drive the isomerization reaction in a bistable potential. The perturbation is treated as a random-phase strong oscillation that shifts the energy barrier. We show how the reaction can be controlled by means of very intense single Gaussian pulses or linear combinations of these pulses and how the control can survive after the perturbing action. The actual resistance to the bath effects changes with the scheme used, and we concentrate on the different behaviors for different bath frequencies. In particular pump-probe schemes offer stabilizing properties at some frequency windows of the bath spectral range. We also address the problem of phase sensitivity and we find the presence of phase nodes, which are particular values of the bath frequency where the reaction dynamics is almost insensitive to the actual phase of the bath oscillations.