This paper proposes a new method for estimating available bandwidth in wireless networks and other networks with random service. Existing bandwidth estimation methods developed for wired networks fail in wireless settings due to the increased variability of wireless channels. The proposed method models the network as a general stationary system using concepts from stochastic network calculus, rather than assuming a work-conserving queueing model. It develops a new approach to bandwidth estimation based on iterative constant-rate probes and statistical inference of an unknown bounding function characterizing network throughput and delays. The method is evaluated for both wired and wireless networks and provides more accurate and reliable estimates than approaches adapted from wired-only models.