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In this paper we consider Bayesian estimation based on bivariate ranked set sample, in which units are ranked based on measurements made on an easily and exactly measurable auxiliary variable X which is correlated with the study variable Y . We obtain Bayes estimator for the scale parameter of the study variate Y , when (X, Y ) follows a Morgenstern type bivariate Rayleigh distribution. The Bayes estimators are considered based on bivariate ranked set sampling, extreme ranked set sampling and maximum ranked set sampling with unequal sample. The accuracy of estimation methods in this paper is illustrated using simulation study. Finally, a real data set is analyzed.