We develop a new method for bias correction of correct order, which models the error of the target estimator as a function of the corresponding bootstrap estimator, and the original estimators and bootstrap estimators when estimating the parameters governing the model underlying the sample. This is achieved by considering a large set of plausible parameter values, generating pseudo original samples and bootstrap samples for each parameter and then searching for an appropriate functional relationship. Under certain conditions, the use of this procedure permits also estimating the MSE of the bias corrected estimators. The method is applied for estimating the prediction MSE in small area estimation of proportions under generalized mixed models. Empirical comparisons with the Jackknife and bootstrap procedures based on a simulation study are presented.