There are many estimators of the bivariate survival function under right censoring. These usually assume non-informative censoring and don't utilize time-dependent covariates. The widely used Dabrowska's estimator (Dabrowska D., 1988) is inconsistent under dependent censoring. We first propose an initial estimator as a generalization of the Dabrowska's estimator that accounts for informative censoring. This initial estimator is guaranteed to improve on Dabrowska's estimator and remains consistent under informative censoring schemes if one estimates the censoring mechanism consistently. We then propose a one-step estimator that provides improvement on our initial estimator and incorporates time-dependent covariate process. This one-step estimator is consistent and asymptotically normal, as long as the censoring mechanism is estimated consistently. We evalute the performance of the estimator under various scenarios with an extensive simulation study.