Multistability is a characteristic that can introduce exceptional versatility in engineered structural systems. For such adaptive structures, multiple stable equilibria empower a means for large shape change, mechanical properties tuning, and dynamic response tailoring, all potentially free from the costs and complexity associated with sustained active controls and hardware. As a result, a comprehensive understanding on the sensitivities of transitioning between the stable equilibria of multistable structures is needed to effectively leverage the valuable adaptation mechanisms. Previous characterizations provided useful insights on the dynamic sensitivities to snapthrough of bi-or multistable structures under either harmonic or stochastic excitations, but the more practical combination of harmonic and stochastic loading has not received close attention. To provide a more complete understanding on the robustness of adaptive, multistable structures under complex excitations, this research explores new methods to quantify the likelihood of triggering the dynamic transitions between stable equilibria in an archetypal, magnetoelastic, bistable cantilever beam due to combined harmonic and stochastic loading. The studies capture the myriad, steady-state dynamic response regimes and susceptibilities of the bistable architecture to suddenly transition to another stable equilibria, or back again, due to various levels of additive white noise in the total excitation spectra. It is discovered that when the harmonic excitation component occurs at a frequency close to the linearized resonance the additional noise excitation rapidly disables the persistent periodic snapthrough dynamics, resulting in locally stable intrawell oscillation. On the other hand, the extra noise may drastically compromise the integrity of locally stable periodic responses that occur at frequencies around one-half of the linearized resonance. By addressing the previous unknowns regarding more realistic excitation spectra, these new insights and assessment methods provide important guidance towards effective implementation of bistable constituents in adaptive structures applications.