The dual form of the massless Schwinger model on the lattice overcomes the complex action problems from two sources: from a topological term, as well as from non-zero chemical potential, making these physically interesting cases accessible to Monte Carlo simulations. The partition function is represented as a sum over fermion loops, dimers and plaquette-surfaces such that all contributions are real and positive. However, these new variables constitute a highly constraint system and suitable update strategies have to be developed. We present an approach based on locally growing plaquette-surfaces surrounded by fermion loop segments combined with a worm based strategy for updating chains of dimers. The update strategy is checked with conventional simulations, analytical results and exact summation on small volumes and we discuss the physical implications of the results.