This paper develops a case study using the process algebra CSP to enable controlled interaction between B machines. This illustrates how B machines are essential components within a combined communicating system. The development steps used to build the case study are new: they are applications of theoretical results which allow us to focus on the external interface of a combined communicating system, compositionally verify it, and show that it is a refinement of a more abstract specification described in CSP. This allows safety and liveness properties to be established for combinations of communicating B machines