Given a masa bimodule M, there is a subset of the direct product of a pair of measure spaces which supports M in a natural way. In this talk we shall consider the question of in what sense the map from a masa bimodule to its support is continuous. Our approach is based on a continuity result of Victor Shulman and Ivan Todorov for the map sending a unital subalgebra of B(H) (where H is an infinite dimensional Hilbert space) which contains a masa, to its Invariant Subspace Lattice. We shall discuss some continuity results and counterexamples for the general case, and show that, if we restrict our attention to masa bimodules which are ranges of weak* continuous masa bimodule projections, then much more is possible.