  We consider the task of representing signals supported on graph bundles,
which are generalizations of product graphs that allow for "twists" in the
product structure. Leveraging the localized product structure of a graph
bundle, we demonstrate how a suitable partition of unity over the base graph
can be used to lift the signal on the graph into a space where a product
factorization can be readily applied. Motivated by the locality of this
procedure, we demonstrate that bases for the signal spaces of the components of
the graph bundle can be lifted in the same way, yielding a basis for the signal
space of the total graph. We demonstrate this construction on synthetic graphs,
as well as with an analysis of the energy landscape of conformational manifolds
in stereochemistry.
