The bulk high-temperature superconducting (HTS) undulator shows great potential for being used in a compact free-electron laser, shortening the length of both the undulator system and the linear accelerators. This paper reports on the electromagnetic design study of a 0.6 m-long, 12 mm-period bulk HTS undulator which is considered as an alternative technology for the upgrade of the Shanghai HIgh repetitioN rate XFEL and Extreme light facility (SHINE). The external superconducting solenoid is optimized to provide a background field of up to 7 T with an inhomogeneity <1% within the good field region of ϕ 40 mm × 600 mm. The staggered-array ReBCO bulks are assembled in a 110 mm-diameter bore as a HTS insert, independent of the 7 T superconducting solenoid. The ReBCO bulk superconductors are magnetized using the field-cooled (FC) magnetization approach for the generation of on-axis sinusoidal magnetic field. The 0.6 m-long HTS insert is optimized using the E-J power law based 2D H-formulation method and benchmarked with the 2D A-V formulation based backward computation method, obtaining a maximum undulator field B₀ of 2.33 T with the minimized first and second on-axis field integrals.