We propose a Bayesian approach for constructing gene networks based on microarray data. Especially, we focus on Bayesian methods that can provide soft (probabilistic) information. This soft information is attractive not only for its ability to measure the level of confidence of the solution, but also because it can be used to realize Bayesian data integration, an extremely important task in gene network research. We propose a variable selection formulation of gene regulation and develop an inference solution based on a variational Bayesian expectation maximization (VBEM) learning rule. This solution has better performance and lower complexity than the popular Monte Carlo sampling techniques. In addition, we develop a method to incorporate the often needed constraints into the VBEM algorithm, making it much more suitable for common cases of small data size. To further illustrate the advantage of the VBEM algorithm, we demonstrate a Bayesian data integration scheme using the soft information obtained from the VBEM algorithm. The efficacy of the proposed VBEM algorithm and the corresponding Bayesian data integration scheme is evaluated on both simulated data and the yeast cell cycle microarray data sets.