Generating mu and Bmu in models with Dirac Gauginos

We consider the extension of the Minimal Supersymmetric Standard Model by Dirac masses for the gauginos. We study the possibility that the same singlet that pairs up with the bino, to form a Dirac fermion, is used to generate mu and Bmu terms through its vacuum expectation value. For this purpose, we assume that, in the Higgs potential, the necessary R-symmetry breaking originates entirely from a superpotential term cubic in the singlet and discuss the implications for the spectrum of the model.