Ultrasonic Guided Waves (UGWs) play a vital role in the non-destructive testing due to exceptional sensitivity to small damage. This study proposes an integrated two-stage Bayesian inference scheme, aimed at updating the physical model parameters of the rail, to improve subsequent crack identification, thus overcoming the limitations caused by insufficient crack detection due to modeling discrepancies. Within the integrated two-stage Bayesian inference framework, the physical model parameters (i.e., modulus of elasticity and damping loss factor, etc.) are updated using wavenumbers extracted from UGW measurements. Subsequently, the crack parameters are identified based on scattering coefficients predicted by the updated forward solver. An integral formula is ultimately derived analytically to incorporate the uncertainty propagation procedure from the physical model parameters into the crack parameter identification, properly accounting for the model parameter variability. Additionally, a Monte Carlo simulation is employed to approximate the integral. To address the computational challenges in the likelihood evaluations during the Bayesian inversion procedure using Transitional Markov Chain Monte Carlo (TMCMC) in both stages, a cost-effective Kriging predictor providing a surrogate mapping between the model predictions and the identified parameters is established for each stage based on the training outputs computed using an advanced wave propagation simulation scheme. The feasibility and effectiveness are verified through numerical and experimental investigations. Results indicate that the proposed Bayesian inference scheme based on UGWs in conjunction with the wave propagation simulation-aided metamodel can identify the location and size of the crack with reasonable accuracy and efficiency. The proposed scheme could result in more reliable models effectively enhancing the accuracy of crack identification.