We introduce a notion of bimodule in the setting of enriched ∞-categories, and use this to construct a double ∞-category of enriched ∞-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 (∞,2)-category of enriched ∞-categories with functors as 1-morphisms the 2-morphisms are given by natural transformations