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Additive manufacturing (AM) enables the fabrication of complex, highly customized geometries. However, the design and fabrication of structures with advanced functionalities, such as multistability and fail-safe mechanism, remain challenging due to the significant time and costs required for high-fidelity simulations and iterative prototyping. In this study, we investigate the application of Bayesian Optimization (BO), an advanced machine learning framework, to accelerate the discovery of optimal AM compatible designs with such advanced properties. BO uses a probabilistic surrogate to strategically balances the exploration of design space with few test designs and the exploitation of design space near current best performing designs, thereby reducing the number of design simulations needed. While existing studies have demonstrated the potential of BO in AM, most have focused on static or simple designs. Here, we target multistable structures that can reconfigure among multiple stable states in response to external conditions. Since mechanical performance (e.g., strength) is configuration-dependent, our goal is to identify high performing designs while ensuring that strength in all stable configurations exceeds a prescribed threshold for structural robustness.