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Josephson junctions with weak links of exotic materials allow the elucidation of the Josephson effect in previously unexplored regimes. Further, such devices offer a direct probe of novel material properties, for example, in the search for Majorana fermions. In this paper, we report on dc and ac Josephson effect of high-mobility, hexagonal boron nitride encapsulated graphene Josephson junctions. On the application of rf radiation, we measure phase-locked Shapiro steps. An unexpected bistability between ±1 steps is observed with switching times on the order of seconds. A critical scaling of the bistable state is measured directly from the switching time, allowing for direct comparison to numerical simulations. We show such intermittent chaotic behavior is a consequence of the nonlinear dynamics of the junction and has a sensitive dependence on the current-phase relation. This paper draws connections between nonlinear phenomena in dynamical systems and their implications for ongoing condensed matter experiments exploring topology and exotic physics.