The special band structure of three-dimensional Dirac semimetal (3D DSM) makes it show strong nonlinear optical characteristics in the terahertz region, which provides a new way to develop terahertz nonlinear devices with low threshold. In this paper, we theoretically study the optical bistability (OB) of transmitted light in a multilayer structure with 3D DSM embedded in two one-dimensional photonic crystals (1D PhC). The topological edge state (TES) excited by the 1D PhC heterostructure significantly enhances the local electric field near the nonlinear 3D DSM, which provides a positive condition for the realization of low threshold OB. Through parameter optimization, we obtain a threshold electric field with an incident electric field of 106 V/m levels. Furthermore, the influences of the Fermi energy and thickness of 3D DSM and the angle of the incident light on the hysteretic behavior as well as the threshold of OB are clarified. 3D DSM-based optical devices with intrinsic OB provide a building block for future integrated optical and all-optical networks.