The viability of hydrogen storage in bedded salt caverns hinges on understanding the geomechanical challenges posed by the anisotropic stress states and complex geology of such environments. This study presents a comprehensive geomechanical analysis focusing on a proposed cavern within the Carribuddy Formation in Western Australia, characterized by its interbedded salt layers. This paper introduces a new geomechanical workflow, encompassing 1D and 3D modeling techniques to provide detailed changes of mechanical properties and stress state in interbedded salt formation allowing to identify the initial optimal operational pressures for underground hydrogen storage. Initial 1D models evaluated mechanical properties and in-situ stresses, while subsequent 3D simulations, enriched by data from neighboring wells, detailed the stress, strain, and displacement responses of the cavern walls to internal pressure changes. The analysis pinpointed an initial safe gas pressure range between 3000 and 4000 psi, attributing this margin to the robust characterization of the mechanical and in-situ stress of the formation. Our findings underscore the significance of high-resolution geomechanical modeling in identifying initial optimal operational pressures for hydrogen storage in salt caverns, ensuring both safety and structural integrity.