Variational Bayes (VB) refers to a framework used to make fast deterministic approximations to the posterior density for Bayesian statistical inference. Traditionally, it has competed with Markov Chain Monte Carlo (MCMC) methods, a stochastic method which is asymptotically correct but computationally expensive. We derive the VB approximation to the Directed Clustered Latent Preference Network Model, which is inspired by ideas from Hoff et al. (2002); Handcock et al. (2007); Ward and Hoff (2007); Salter-Townshend and Murphy (2013); Krivitsky and Handcock (2008). The model handles binary-valued or continuous directed network data, and incorporates Gaussian mixture models over the separate latent sending and receiving preference spaces of each actor. We apply the model to simulated and real datasets to evaluate its performance against existing MCMC methods such as the Gibbs sampler. We discover new insights in the well-studied Sampson's Monks dataset (Sampson, 1968), as well as confirm existing results with the Correlates of War International Trade dataset (Barbieri and Keshk, 2012). We conclude by discussing unresolved issues, potential solutions, and areas of future work.