A point process on a set is a random bag of elements of that set. In this extended abstract we explore programming with point processes in a monadic style. To this end we identify point processes on a set X with probability measures of bags of elements in X. We describe this view of point processes using the composition of the Giry and bag monads in the category Meas of measurable spaces and functions. We prove that this composition also forms a monad using the distributive law for monads.