We explore optical bistability and degenerate four-wave mixing of a hybrid optical system composed of a photonic crystal nanocavity, a single nitrogen-vacancy center embedded in the cavity, and a nearby photonic waveguide serving for in- and outcoupling of light into the cavity in the weak-coupling regime. Here the hybrid system is coherently driven by a continuous-wave bichromatic laser field consisting of a strong control field and a weak probe field. We take account of the nonlinear nature of the nitrogen-vacancy center in the Heisenberg-Langevin equations and give an effective perturbation method to deal with such problems in the continuous-wave-operation regime. The results clearly show that the bistability region of the population inversion and the intensity of the generated four-wave mixing field can be well controlled by properly adjusting the system practical parameters. The nanophotonic platform can be used to implement our proposal. This investigation may be useful for gaining further insight into the properties of solid-state cavity quantum electrodynamics system and find applications in all-optical wavelength converter and switch in a photonic crystal platform.