We describe a fully Bayesian approach to grapheme-to-phoneme conversion based on the joint-sequence model (JSM). Usually, standard smoothed n-gram language models (LM, e.g. Kneser-Ney) are used with JSMs to model graphone sequences (joint grapheme-phoneme pairs). However, we take a Bayesian approach using a hierarchical Pitman-Yor-Process LM. This provides an elegant alternative to using smoothing techniques to avoid over-training. No held-out sets and complex parameter tuning is necessary, and several convergence problems encountered in the discounted Expectation-Maximization (as used in the smoothed JSMs) are avoided. Every step is modeled by weighted finite state transducers and implemented with standard operations from the OpenFST toolkit. We evaluate our model on a standard data set (CMUdict), where it gives comparable results to the previously reported smoothed JSMs in terms of phoneme-error rate while requiring a much smaller training/testing time. Most importantly, our model can be used in a Bayesian framework and for (partly) un-supervised training.