The detection of driving events could be useful for reducing accidents, fleet management and insurance premiums etc. Currently, top of the range vehicles and large fleets employ expensive driver monitoring systems. However, most drivers do not have access to such systems. The required monitoring platform would have to deliver the required performance while also being affordable and accessible. A candidate with considerable promise is the smartphone with sensors built-in that could be exploited for the detection of driving events. However, to date it has not been possible to achieve the required correct, missed and false detection rates in addition to the computational efficiency for real-time operations. This paper proposes a novel bagging tree and dynamic time warping (DTW) integrated algorithm for the detection of driving events employing acceleration and orientation data from a smartphone's low cost three-axis accelerometers and gyroscopes. The bagging tree-based machine learning algorithm provides the initial maneuver detection results, as well as the location of the event start and end points. Event detection is then achieved by calculating the similarity of the results predicted through the bagging tree algorithm with the corresponding templates extracted from the experience datasets, while also applying a number of constraints to verify the calculated results. Field test results show that the proposed integrated algorithm is superior to the state-of-the-art, achieving a high correct detection accuracy of 97.5%, a low missed detection of 2.5% and a false detection rate of 2.9%. The corresponding results for the best alternative candidate method are 90.2%, 9.8% and 11.7%. Furthermore, the improvement in computational efficiency offered by our proposed approach is three to more than ten times greater than that of the other state-of-the-art algorithms.