Predicting the severity and onset of depressive symptoms is of great importance. User-specific models have better performance than a general model but require significant amounts of training data from each individual, which is often impractical to obtain. Even when this is possible, there is a significant lag between the beginning of the data-collection phase and when the system is completely trained and thus able to start making useful predictions. In this study, we propose a transfer learning Bayesian modelling method based on a Markov Chain Monte Carlo (MCMC) sampler and Bayesian model averaging for dealing with the challenge of building user-specific predictive models able to make predictions of self-reported well-being scores with limited sparse training data. The evaluation of our method using real-world data collected within the NEVERMIND project showed a better predictive performance for the transfer learning model compared to conventional learning with no transfer.