In this paper, we present a novel statistical convergence analysis for bilinear parameter estimators. We account for two variations of a two-stage separation technique introduced by Bai [1], where the variations differ in the second stage. It turns out for both estimators that the probability of a large error decreases as the inverse square root of the number of measurements. We numerically demonstrate the estimators' performance by solving a water leak localization problem involving bilinear parameter estimation.