A bipartite graph G = ( A , B , E ) is said to be a biconvex bipartite graph if there exist orderings < A in A and < B in B such that the neighbors of every vertex in A are consecutive with respect to < B and the neighbors of every vertex in B are consecutive with respect to < A . A caterpillar is a tree that will result in a path upon deletion of all the leaves. In this paper, we prove that there exists a spanning caterpillar in any connected biconvex bipartite graph . Besides being interesting on its own, this structural result has other consequences. For instance, this directly resolves the burning number conjecture for biconvex bipartite graphs.