Traditionally, bulk nanocomposites of electrically conducting particles and insulating polymers have been categorized as either insulating or conducting when the nanoparticle concentration is below or above the percolation threshold, respectively. Meanwhile, thin-film polymer nanocomposites can exhibit resistive switching behavior appropriate for digital memory applications. Here, we present the first report of reversible resistive switching in bulk, glassy polymer nanocomposites. At compositions close to the electrical percolation threshold measured at low voltage, silver nanowire-polystyrene nanocomposites demonstrate reversible resistive switching with increasing voltage at room temperature. Nanocomposites with compositions outside of this range exhibit either irreversible switching, or no switching at all. We propose that resistive switching in these materials is the result of the field-induced formation of silver filaments that bridge adjacent nanowire clusters, extending the percolation network and decreasing the sample's bulk resistivity. These findings break from the usual dichotomy of insulating or conducting properties in polymer nanocomposites and could inspire new devices that capitalize on this responsive behavior in these versatile materials.