We conduct a theoretical study of the bistable optical response of a nanoparticle heterodimer comprised of a closely spaced semiconductor quantum dot and a metal nanoparticle. The bistable nature of the response results from the interplay between the quantum dot's optical nonlinearity and its self-action (feedback) originating from the presence of the metal nanoparticle. The feedback is governed by a complex valued coupling parameter G = G(R) + iG(I). We calculate the bistability phase diagram within the system's parameter space: spanned by G(R), G(I), and Δ, the latter being the detuning between the driving frequency and the transition frequency of the quantum dot. Additionally, switching times from the lower stable branch to the upper one (and vice versa) are calculated as a function of the intensity of the driving field. The conditions for bistability to occur can be realized, for example, for a heterodimer comprised of a closely spaced CdSe (or CdSe/ZnSe) quantum dot and a gold nanosphere.