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Like many other clinical and economic studies, each subject of our motivating transplant study is at risk of recurrent events of non-fatal tissue rejections as well as the terminating event of death due to total graft rejection. For such studies, our model and associated Bayesian analysis aim for some practical advantages over competing methods. Our semiparametric latent-class-based joint model has coherent interpretation of the covariate (including race and gender) effects on all functions and model quantities that are relevant for understanding the effects of covariates on future event trajectories. Our fully Bayesian method for estimation and prediction uses a complete specification of the prior process of the baseline functions. We also derive a practical and theoretically justifiable partial likelihood-based semiparametric Bayesian approach to deal with the analysis when there is a lack of prior information about baseline functions. Our model and method can accommodate fixed as well as time-varying covariates. Our Markov Chain Monte Carlo tools for both Bayesian methods are implementable via publicly available software. Our Bayesian analysis of transplant study and simulation study demonstrate practical advantages and improved performance of our approach.