We propose and demonstrate a novel architecture for on-the-fly inference while collecting data from sparse sensor networks. In particular, we consider source localization using acoustic sensors dispersed over a large area, with the individual sensors located too far apart for direct connectivity. An Unmanned Aerial Vehicle (UAV) is employed for collecting sensor data, with the UAV route adaptively adjusted based on data from sensors already visited, in order to minimize the time to localize events of interest. The UAV therefore acts as a information-seeking data mule, not only providing connectivity, but also making Bayesian inferences from the data gathered in order to guide its future actions. The system we demonstrate has a modular architecture, comprising efficient algorithms for acoustic signal processing, routing the UAV to the sensors, and source localization. We report on extensive field tests which not only demonstrate the effectiveness of our general approach, but also yield specific practical insights into GPS time synchronization and localization accuracy, acoustic signal and channel characteristics, and the effects of environmental phenomena.