Bell nonlocality is an intrinsic feature of quantum mechanics, which can be detected via the violation of Bell inequalities. It is therefore a fundamental question to certify Bell nonlocality from experimental data. Here, we present an optimization framework to detect Bell-operator correlations by exploring flexible mappings between Bell inequalities and Hamiltonians corresponding to the Bell operators. We show that several Hamiltonian models can be mapped to new inequalities with improved classical bounds compared to the original one, enabling a more robust certification of Bell-operator correlations. From the other direction, we investigate the mapping from fixed Bell inequalities to Hamiltonians, aiming to maximize quantum violations while considering experimental imperfections. As a practical application, we experimentally exploit this method in an XXZ-like honeycomb-lattice model utilizing over $70$ superconducting qubits. The successful application of this technique, as well as combining the two directions to form an optimization loop, may open new avenues for developing more practical and noise-resilient certification techniques for Bell-operator correlations and enable broader experimental explorations.