BSE Banach modules and bundles of Banach spaces

In a recent paper, S.-E. Takahasi defined the notion of a BSE Banach module over a commutative Banach algebra A with bounded approximate identify. We show that the multiplier space M(X) of X can be represented as a space of sections in a bundle of Banach spaces, and we use bundle techniques to obtain shorter proofs of various of Takahasi's results on C*-algebra modules and to answer several questions which he raised.