Let C be a smooth, proper curve over Fq and sheaf of orders D on C whose generic fiber D is a quaternion algebra over Fq(C). A D-bundle is now a sheaf on C, finite locally free of rank 1 over D. The moduli space and related objects like the Hecke- and shtuka stacks of these D-bundles have been used by several authors, usually under some restrictions, e.g. that D be a sheaf of maximal orders. We generalize the setting to hereditary orders and construct several moduli spaces for these objects. We then prove that the self-intersection number of so-called Heegner-Drinfeld cycles in a suitable ambient stack is computable via the trace of a correspondence acting on the cohomology of a certain DM-stack.