In order to answer how much bandwidth is available to an application from one end to another in a network, state-of-the-art estimation techniques, based on active probing, inject artificial traffic with a known structure into the network. At the receiving end, the available bandwidth is estimated by measuring the structural changes in the injected traffic, which are caused by the network path. However, bandwidth estimation becomes difficult when packet distributions are distorted by non-fluid bursty cross traffic and multiple links. This eventually leads to an estimation bias. One known approach to reduce the bias in bandwidth estimations is to probe a network with constant-rate packet trains and measure the average structural changes in them. However, one cannot increase the number of packet trains in a designated time period as much as needed because high probing intensity overloads the network and results in packet losses in probe and cross traffic, which distorts probe packet gaps and inflicts more bias. In this work, we propose a machine learning-based, particularly classification-based, method that provides reliable estimates utilizing fewer packet trains. Then, we implement supervised learning techniques. Furthermore, considering the correlated changes over time in traffic in a network, we apply filtering techniques on estimation results in order to track the changes in the available bandwidth. We set up an experimental testbed using the Emulab software and a dumbbell topology in order to create training and testing data for performance analysis. Our results reveal that our proposed method identifies the available bandwidth significantly well in single-link networks as well as networks with heavy cross traffic burstiness and multiple links. It is also able to estimate the available bandwidth in randomly generated networks where the network capacity and the cross traffic intensity vary substantially. We also compare our technique with the others that use direct probing and regression approaches, and show that ours has better performance in terms of standard deviation around the actual bandwidth values.