The difference in restricted mean survival time (dRMST) at a specific time point is an appropriate measure to quantify the treatment effect between two arms in randomized clinical trials when the proportional hazards assumption does not hold. This is common in the context of immuno-oncology therapies. Several frequentist methods exist to estimate RMST based on modeling and integrating the survival function. A more natural approach is to consider a regression model on the RMST directly using pseudo-observations which allows for a direct fit without modeling the survival function. This approach also has the advantage of extending the analysis for single time point of interest to the joint analysis at multiple time points. Only two Bayesian methods exist, and both model the survival function with a nonparametric prior process. We develop a new Bayesian method based on pseudo-observations and the generalized method of moments (GMM) that offers RMST estimation adjusted on covariates without the need to model the survival function, making it attractive compared to existing Bayesian methods. A simulation study of 2-arms randomized clinical trials with different time-dependent treatment effects and covariates effects was conducted, demonstrating that this new approach yields valid results, consistent with existing methods, and shows improved precision after covariates adjustment. For illustration, the methods were applied for analyzing the PSA progression-free survival of the Getug-AFU 15 trial, a randomized, open-label, phase 3 trial comparing an androgen-deprivation therapy alone or with docetaxel in non-castrate metastatic prostate cancer. This illustration also demonstrates the advantage of this new method to perform RMST analysis with covariates adjustment in the Bayesian framework.