The problem of computing bandwidth guaranteed paths for given flow requests in an ad-hoc network is complicated because neighboring links share the medium. We define the path width on top of the conflict-graph based interference model, and present the Ad-Hoc Shortest Widest Path (ASWP) routing problem in an ad-hoc network context. We propose a distributed algorithm to address the ASWP problem. Adopting the Bellman-Ford architecture and the k-shortest-path approach, the proposed algorithm achieves a performance close to the optimum. Numerical simulations demonstrate the performance of the algorithm, and also analyze gains achieved over prevalent shortest-path algorithms.