Wireless sensor networks have become an important and promising research area during the last recent years. Clock synchronization is one of the areas that play a crucial role in the design, implementation, and operation of wireless sensor networks. Under the assumption that there is no clock skew between sensor nodes, the Maximum Likelihood Estimate (MLE) of clock offset was proved by  for clock synchronization protocols that assume exponential random delays and a two-way message exchange mechanism such as TPSN (Timing-sync Protocol for Sensor Networks ). This MLE is asymptotically unbiased. However, the estimator is biased in the presence of a finite number of samples and much more biased in asymmetric random delay models, where the upstream delay characteristics are different from the downstream delay characteristics, and thus its performance is deteriorated. This paper proposes clock offset estimators based on the bootstrap bias correction approach, which estimates and corrects the bias of the MLE in the exponential delay model, and hence it results in better performances in mean squared error (MSE).