Cavity-enhanced thermo-optic bistability is studied in a graphene-on-Si3N4 ring resonator. By engineering the coverage of the monolayer graphene on top of the Si3N4 ring resonator, we observed a two-fold enhancement in the thermo-optically induced resonance shift rate and an 18-fold increase in the effective thermal nonlinear refractive index compared with the devices without graphene. The thermo-optic hysteresis loop was also characterized in this hybrid structure, where the experimental results agree well with the theoretical calculations. This Letter paves the way for graphene-on-Si3N4-based high-speed photodetectors, modulators, and devices for on-chip nonlinear optical applications.