Gestures in music are of paramount importance partly because they are directly linked to musicians' sound and expressiveness. At the same time, current motion capture technologies are capable of detecting body motion/gestures details very accurately. We present a machine learning approach to automatic violin bow gesture classification based on Hierarchical Hidden Markov Models (HHMM) and motion data. We recorded motion and audio data corresponding to seven representative bow techniques (Dotache, Martele, Spiccato, Ricochet, Sautille, Staccato, and Bariolage) performed by a professional violin player. We used the commercial Myo device for recording inertial motion information from the right forearm and synchronized it with audio recordings. Data was uploaded into an online public repository. After extracting features from both the motion and audio data, we trained an HHMM to identify the different bowing techniques automatically. Our model can determine the studied bowing techniques with over 94% accuracy. The results make feasible the application of this work in a practical learning scenario, where violin students can benefit from the real-time feedback provided by the system.