A well-known result of Walsh states that if is an ideal triangulation of an atoroidal, acylindrical, irreducible, compact 3-manifold with torus boundary components and has essential edges, then every properly embedded, two-sided, incompressible surface is isotopic to a spun-normal surface in unless is isotopic to a fiber or virtual fiber. For a given manifold that fibers over , it was previously unknown whether there exists an ideal triangulation in which the fiber appears as a spun-normal surface. We prove that such a triangulation exists and give an algorithm to construct the ideal triangulation provided has a single boundary component.