Abstract Meaning Representation (AMR) offers a unified semantic representation for natural language sentences. Thus transformation between AMR and text yields two transition tasks in opposite directions, i.e., Text-to-AMR parsing and AMR-to-Text generation. Existing AMR studies only focus on one-side improvements despite the duality of the two tasks, and their improvements are greatly attributed to the inclusion of large extra training data or complex structure modifications which harm the inference speed. Instead, we propose data-efficient Bidirectional Bayesian learning (BiBL) to facilitate bidirectional information transition by adopting a single-stage multitasking strategy so that the resulting model may enjoy much lighter training at the same time. Evaluation on benchmark datasets shows that our proposed BiBL outperforms strong previous seq2seq refinements without the help of extra data which is indispensable in existing counterpart models. We release the codes of BiBL at: https://github.com/KHAKhazeus/BiBL.