It is well known that room temperature ionic liquids (RTILs) often adopt a charge-separated layered structure, i.e. with alternating cation- and anion-rich layers, at electrified interfaces. However, the dynamic response of the layered structure to temporal variations in applied potential is not well understood. We used in situ, real-time x-ray reflectivity to study the potential-dependent electric double layer (EDL) structure of an imidazolium-based RTIL on charged epitaxial graphene during potential cycling as a function of temperature. The results suggest that the graphene-RTIL interfacial structure is bistable in which the EDL structure at any intermediate potential can be described by the combination of two extreme-potential structures whose proportions vary depending on the polarity and magnitude of the applied potential. This picture is supported by the EDL structures obtained by fully atomistic molecular dynamics simulations at various static potentials. The potential-driven transition between the two structures is characterized by an increasing width but with an approximately fixed hysteresis magnitude as a function of temperature. The results are consistent with the coexistence of distinct anion- and cation-adsorbed structures separated by an energy barrier (∼0.15 eV).