  In this article we study covering spaces of symplectic toric orbifolds and
symplectic toric orbifold bundles. In particular, we show that all symplectic
toric orbifold coverings are quotients of some symplectic toric orbifold by a
finite subgroup of a torus. We then give a general description of the labeled
polytope of a toric orbifold bundle in terms of the polytopes of the fiber and
the base. Finally, we apply our findings to study the number of toric
structures on products of labeled projective spaces.
