Our approach aims to integrate gene expression profiles with transcription factor binding data, such as binding motifs in promoter regions or p-values from immunoprecipitation experiments. The model we employ is a mixture of factor analysers, in which the latent variables correspond to different transcription factors, grouped into complexes or modules. We pursue inference in a Bayesian framework, using the Variational Bayesian Expectation Maximization (VBEM) algorithm for approximate inference of the posterior distributions of the model parameters, and estimation of a lower bound on the marginal likelihood for model selection. We have evaluated the performance of the proposed method on three criteria: activity profile reconstruction, gene clustering, and network inference. The objective of the first criterion is to assess whether the activity profiles of the transcriptional regulatory modules can be reconstructed from gene expression data. The second criterion tests whether the method can discover biologically meaningful groupings of genes, indicated by significant enrichment for known gene ontologies. The third criterion addresses the question of whether the proposed scheme can make a useful contribution to computational systems biology, where one is interested in the reconstruction of gene regulatory networks from diverse sources of postgenomic data.