We report observation of optical bistability and enhanced thermal nonlinearity in a graphene-silicon waveguide resonator. Photo-induced Joule heating in the graphene layer gives rise to a temperature increase in the silicon waveguide core and a corresponding thermo-optic shift in the resonance of the Fabry-Perot resonator. Measurement of the nonlinear resonance spectra showed a 9-fold increase in the effective thermal nonlinear index due to the graphene layer compared with a bare silicon waveguide.