Recently, Mobile Crowdsourcing (MC) has aroused great interest on the part of both academic and industrial circles. One of the key problems in MC is designing the proper mechanisms to incentivize user participation, as users are typically self-interested and must consume a substantial amount of MC resources/costs. Although considerable research has been devoted to this problem, the majority of studies have neglected the privacy issue in mechanism design. In this study, we consider the scenario where a mobile crowdsourcing platform aims to maximize the crowdsourcing revenue under a budget constraint, and users are interested in maximizing their utility while keeping their cost private. We design differentially-private mechanisms for such a scenario under an offline setting where users bid their costs simultaneously and under an online setting where user bids are revealed one by one. We show that our mechanisms simultaneously achieve provable performance bounds with respect to several measures, including revenue, differential privacy, truthfulness, and individual rationality. Finally, we also conduct extensive numerical experiments to demonstrate the effectiveness of our approach.