Many methods for end-to-end capacity estimation over wired networks assume that link capacities are constant and that all cross-traffic interaction occurs through queuing delays at node buffers. However, wireless ad hoc networks do not conform to these assumptions due to the shared and unreliable nature of the transmission medium. In this paper we distinguish the concept of end-to-end bandwidth (the maximum rate that can be achieved when the resources along the path are not shared with competing traffic) from that of end-to-end capacity (the minimum transmission rate among the nodes conforming the path) and show that the former is a random variable distributed within some range, which depends on the packet length, among other factors. After developing a simple theoretical framework to compare with, we devise a simple and effective dispersion-based method to estimate the mean end-to-end bandwidth for any packet length. The method is shown to be efficient, to converge quickly to an accurate estimate for any packet length, to be robust against cross-traffic, and to timely track bandwidth variations.