In biology, more and more information about the interactions in regulatory systems becomes accessible, and this often leads to prior knowledge for recent data interpretations. In this work we focus on multivariate signaling data, where the structure of the data is induced by a known regulatory network. To extract signals of interest we assume a blind source separation (BSS) model, and we capture the structure of the source signals in terms of a Bayesian network. To keep the parameter space small, we consider stationary signals, and we introduce the new algorithm emGrade, where model parameters and source signals are estimated using expectation maximization. For network data, we find an improved estimation performance compared to other BSS algorithms, and the flexible Bayesian modeling enables us to deal with repeated and missing observation values. The main advantage of our method is the statistically interpretable likelihood, and we can use model selection criteria to determine the (in general unknown) number of source signals or decide between different given networks. In simulations we demonstrate the recovery of the source signals dependent on the graph structure and the dimensionality of the data.