Recent years have witnessed the proliferation of mobile crowd sensing (MCS) systems that leverage the public crowd equipped with various mobile devices (e.g., smartphones, smartglasses, smartwatches) for large scale sensing tasks. Because of the importance of incentivizing worker participation in such MCS systems, several auction-based incentive mechanisms have been proposed in past literature. However, these mechanisms fail to consider the preservation of workers' bid privacy. Therefore, different from prior work, we propose a differentially private incentive mechanism that preserves the privacy of each worker's bid against the other honest-but-curious workers. The motivation of this design comes from the concern that a worker's bid usually contains her private information that should not be disclosed. We design our incentive mechanism based on the single-minded reverse combinatorial auction. Specifically, we design a differentially private, approximately truthful, individual rational, and computationally efficient mechanism that approximately minimizes the platform's total payment with a guaranteed approximation ratio. The advantageous properties of the proposed mechanism are justified through not only rigorous theoretical analysis but also extensive simulations.