Bayesian inference is applied to the core-quasiparticle coupling (CQPC) model with Metropolis-Hastings Markov chain Monte Carlo sampling to quantify the uncertainties of the principal moments of inertia (MoIs) for wobbling in ${}^{135}Pr$. Using only the experimental yrast and wobbling energies as constraints, the MoI posterior supports the ordering ${\Im }_m>{\Im }_s>{\Im }_l$ and reveals correlations among the three parameters. Propagating the posterior yields credible intervals for the energy spectra and, as predictions at fixed electromagnetic inputs, for transition probabilities and angular momentum geometry. Within the energy compatible MoI region, the decrease-then-increase of the wobbling energy and the angular-momentum geometry remain stable, supporting a robust transverse-to-longitudinal evolution. This work provides a practical Bayesian protocol for assessing the statistical robustness of odd-$A$ wobbling interpretations in the CQPC model.