Bimodules and natural transformations for enriched $infty$-categories

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.