Computer-coded verbal autopsy (CCVA) algorithms predict cause of death from high-dimensional family questionnaire data (verbal autopsies) of a deceased individual. CCVA algorithms are typically trained on non-local data, then used to generate national and regional estimates of cause-specific mortality fractions. These estimates may be inaccurate if the non-local training data is different from the local population of interest. This problem is a special case of transfer learning which is now commonly deployed for classification within a target domain (e.g. a particular population) with training performed in data from a source domain (a different population). We present a parsimonious hierarchical Bayesian transfer learning framework using any baseline classifier trained on source domain data, and a relatively small labeled target domain dataset. We introduce a shrinkage prior for the transfer error rates guaranteeing that, in absence of any labeled target domain data or when the baseline classifier is perfectly accurate, the domain-adapted (calibrated) estimate coincides with the naive estimate from the baseline classifier, thereby subsuming the default practice as a special case. A Gibbs sampler using data augmentation enables fast implementation. We then extend our approach to use an ensemble of baseline classifiers. Theoretical and empirical results demonstrate how the ensemble model favors the most accurate baseline classifier. Simulated and real data analyses reveal dramatic improvement in verbal autopsy analysis using our transfer learning approach.