  We introduce a notion of bimodule in the setting of enriched
$\infty$-categories, and use this to construct a double $\infty$-category of
enriched $\infty$-categories where the two kinds of 1-morphisms are functors
and bimodules. We then consider a natural definition of natural transformations
in this context, and show that in the underlying $(\infty,2)$-category of
enriched $\infty$-categories with functors as 1-morphisms the 2-morphisms are
given by natural transformations.
