Determining causality plays a fundamental role in scientific discovery and innovation, but it often proves difficult or infeasible to experimentally derive such relationships. Traditionally methods for learning causal relations from observational data have focused on conditional independency tests between variables in a network. More recently, methods focusing on the bivariate case where algorithms determine cause from effect through asymmetries in the data derived from functional assumptions have become popular. In our work, we assume additive noise for the bivariate case and score all possible models using a robust Bayesian model scoring function. We test our method against the Tubïngen cause-effect pairs benchmark dataset and achieve moderate results demonstrating the promise of Bayesian methods in functional causal discovery.