B0-VPG graphs are intersection graphs of axis-parallel line segments in the plane. We show that all AT-free outerplanar graphs are B0-VPG. In the course of the argument, we show that any AT-free outerplanar graph can be identified as an induced subgraph of a 2-connected outerplanar graph whose weak dual is a path. Our B0-VPG drawing procedure works for such graphs and has the potential to be extended to larger classes of outerplanar graphs.