Bayesian optimization is a powerful machine learning technique for solving experimental design problems. With its use in industrial design optimization, time and cost of industrial processes can be reduced significantly. However, often the experimenters in industries may not have the expertise of optimization techniques and may require help from third-party optimization services. This can cause privacy concerns as the optimized design of an industrial process typically needs to be kept secret to retain its competitive advantages. To this end, we propose a novel Bayesian optimization algorithm that can allow the experimenters from an industry to utilize the expertise of a third-party optimization service in privacy preserving manner. Privacy of our proposed algorithm is guaranteed under a modern privacy preserving framework called Error Preserving Privacy, especially designed to maintain high utility even under the privacy restrictions. Using several benchmark optimization problems as well as optimization problems from real-world industrial processes, we demonstrate that the optimization efficiency of our algorithm is comparable to the non-private Bayesian optimization algorithm and significantly better than its differential privacy counterpart.