Uncovering transcription factor (TF) mediated regulatory networks from microarray expression data and prior knowledge is considered in this paper. Bayesian factor models that models direct TF regulation are formulated. To address the enormous computational complexity of the factor for modeling large networks, a novel, efficient basis-expansion factor (BE-FaM) model has been proposed, where the loading (regulatory) matrix is modeled as an expansion of basis functions of much lower dimension. Great reduction is achieved with BE-FaM as the inference involves instead estimation of expansion coefficients with much reduced dimensions. We also address the issue of incorporating the prior knowledge of TF regulation to constrain the factor loading matrix. A Gibbs sampling solution has been developed to estimate the unknowns. The proposed model was validated by the simulation and then applied to the genomic data of the breast cancer to uncover the corresponding TF regulatory networks.