With the rich set of embedded sensors installed in smartphones, we are witnessing the emergence of many innovative commercial mobile crowdsensing applications, which combine the power of mobile technology with crowdsourcing to effectively collect time-sensitive and location-dependent information. Motivated by these real-world applications, we consider the distributed task selection problem for heterogeneous users with different initial locations, destinations, costs, speeds, and reputation levels. We design a Bayesian asynchronous task selection (BATS) algorithm to help the users plan their task selections based on the incomplete information of the task popularity statistics. We prove its convergence and characterize the computation time for the users' updates. As a performance benchmark, we consider the ideal case that the service provider centrally allocates the tasks to the users for social surplus maximization. We show that it is an NP-hard problem and propose a greedy centralized algorithm with a lower complexity as the benchmark performance. Simulation results suggest that the BATS scheme achieves the highest Jain's fairness index and coverage, while yielding a user payoff similar to that with the greedy centralized benchmark. Finally, we evaluate the schemes based on some real-world movement time and distance data from Google Maps.