Mobile crowd sensing (MCS) has emerged as an increasingly popular sensing paradigm due to its cost-effectiveness. This approach relies on platforms to outsource tasks to participating workers when prompted by task publishers. Although incentive mechanisms have been devised to foster widespread participation in MCS, most of them focus only on static tasks (i.e., tasks for which the timing and type are known in advance) and do not protect the privacy of worker bids. In a dynamic and resource-constrained environment, tasks are often uncertain (i.e., the platform lacks a priori knowledge about the tasks) and worker bids may be vulnerable to inference attacks. This paper presents an incentive mechanism HERALD*, that takes into account the uncertainty and hidden bids of tasks without real-time constraints. Theoretical analysis reveals that HERALD* satisfies a range of critical criteria, including truthfulness, individual rationality, differential privacy, low computational complexity, and low social cost. These properties are then corroborated through a series of evaluations.