In this article, we study several properties such as marginal and conditional distributions, joint moments, and mixture representation of the bivariate generalization of the Kummer-Beta distribution. To show the behavior of the density function, we give some graphs of the density for different values of the parameters. Finally, we derive the exact and approximate distribution of the product of two random variables which are distributed jointly as bivariate Kummer-Beta. The exact distribution of the product is derived as an infinite series involving Gauss hypergeometric function, whereas the beta distribution has been used as an approximate distribution. Further, to show the closeness of the approximation, we have compared the exact distribution and the approximate distribution by using several graphs. An application of the results derived in this article is provided to visibility data from Colombia.