Models optimized for accuracy on single images are often prohibitively slow to run on each frame in a video. Recent work exploits the use of optical flow to warp image features forward from select keyframes, as a means to conserve computation on video. This approach, however, achieves only limited speedup, even when optimized, due to the accuracy degradation introduced by repeated forward warping, and the inference cost of optical flow estimation. To address these problems, we propose a new scheme that propagates features using the block motion vectors (BMV) present in compressed video (e.g. H.264 codecs), instead of optical flow, and bi-directionally warps and fuses features from enclosing keyframes to capture scene context on each video frame. Our technique, interpolation-BMV, enables us to accurately estimate the features of intermediate frames, while keeping inference costs low. We evaluate our system on the CamVid and Cityscapes datasets, comparing to both a strong single-frame baseline and related work. We find that we are able to substantially accelerate segmentation on video, achieving near real-time frame rates (20+ frames per second) on large images (e.g. 960 x 720 pixels), while maintaining competitive accuracy. This represents an improvement of almost 6x over the single-frame baseline and 2.5x over the fastest prior work.