Mobile video traffic accounted for more than half of all mobile data traffic over the past two years. Due to the limited bandwidth, users demand for high-quality video streaming becomes a challenge, which could be addressed by exploiting the emerging diversity of access network and adaptive video streaming. In this paper, a network selection algorithm is proposed for Dynamic Adaptive Streaming over HTTP (DASH), the famous international standard on video streaming, to enhance the received video quality to a "multi-homed user" equipped with multiple interfaces. A Multi-Armed Bandit (MAB) heuristic is proposed for a dynamic selection of the best interface at each step. While the Adaptive Bitrate Rules (ABR) used in DASH allow the video player client to dynamically pick the bit rate level according to the perceived network conditions, at each switching step a quality degradation may occur due to the difference in network conditions of the available interfaces. This paper aims to close this gap by (i) designing a MAB algorithm over DASH for a multi-homed user, (ii) evaluating the proposed mechanism through a test-bed implementation, (iii) extending the classic MAB model and (iv) discussing some open issues.