We consider the applicability of Bayesian networks (BNs) for discovering relations between genes, environment, and disease. Most state-of-the-art BN structure learning algorithms are not capable of learning structures from data containing missing values, which is a norm in genetic epidemiological data. In addition, there exists a wealth of existing prior knowledge which could be incorporated to improve computational efficiency in BN structure learning. To address these challenges, we applied a Markov chain Monte Carlo based BN structure learning algorithm to data from a population-based study of bladder cancer in New Hampshire, USA. A large improvement in computational efficiency is achieved under this approach.