Existing localization approaches utilizing environment-specific channel state information (CSI) excel under specific environment but struggle to generalize across varied environments. This challenge becomes even more pronounced when confronted with limited training data. To address these issues, we present the Bayes-Optimal Meta-Learning for Localization (BOML-Loc) framework, inspired by the PAC-Optimal Hyper-Posterior (PACOH) algorithm. Improving on our earlier MetaLoc~\cite{MetaLoc}, BOML-Loc employs a Bayesian approach, reducing the need for extensive training, lowering overfitting risk, and offering per-test-point uncertainty estimation. Even with very limited training tasks, BOML-Loc guarantees robust localization and impressive generalization. In both LOS and NLOS environments with site-surveyed data, BOML-Loc surpasses existing models, demonstrating enhanced localization accuracy, generalization abilities, and reduced overfitting in new and previously unseen environments.