Burst suppression is an inactivated brain state in which the electroencephalogram is characterized by intermittent periods of isoelectric quiescence. Recent modeling studies have suggested an important role for brain metabolic processes in governing the very slow time scales that underlie the duration of bursts and suppressions. In these models, a reduction in metabolism leads to substrate depletion and consequent suppression of action potential firing. Such a mechanism accounts for the appearance of burst suppression when metabolism is directly downregulated. However, in many cases such as general anesthesia, metabolic downregulation occurs in part as a homeostatic consequence of reduced neuronal activity. Here, we develop a mean-field model for neuronal activity with metabolic homeostatic mechanisms. We show that with such mechanisms, a simple reduction in neuronal activity due, for example, to increased neuronal inhibition, will give rise to bistability due to a bifurcation in the combined neuronal and metabolic dynamics. The model reconciles a purely metabolic mechanism for burst suppression with one that includes important dynamical feedback from the neuronal activity itself. The resulting fast-slow dynamical description forms a useful model for further development of novel methods for managing burst suppression clinically.