  In this article, we will give a characterization of Banach bimodules over
$C^*$-algebras of compact operators that arises from operator spaces as well as
a characterization of (F)-Banach bundles amongst all (H)-Banach bundles over a
hyper-Stonian space. These two characterizations are concerned with whether
certain natural map from a Banach bimodule to its canonical bidual is isometric
(we call such bimodule \emph{regular}).
