We consider bi-objective ranking and selection problems, where the goal is to correctly identify the Pareto optimal solutions among a finite set of candidates for which the two objective outcomes have been observed with uncertainty (e.g., after running a multiobjective stochastic simulation optimization procedure). When identifying these solutions, the noise perturbing the observed performance may lead to two types of errors: solutions that are truly Pareto-optimal can be wrongly considered dominated, and solutions that are truly dominated can be wrongly considered Pareto-optimal. We propose a novel Bayesian bi-objective ranking and selection method that sequentially allocates extra samples to competitive solutions, in view of reducing the misclassification errors when identifying the solutions with the best expected performance. The approach uses stochastic kriging to build reliable predictive distributions of the objective outcomes, and exploits this information to decide how to resample. Experimental results show that the proposed method outperforms the standard allocation method, as well as a well-known the state-of-the-art algorithm. Moreover, we show that the other competing algorithms also benefit from the use of stochastic kriging information; yet, the proposed method remains superior.