The estimated average treatment effect in observational studies is biased if the assumptions of ignorability and overlap are not satisfied. To deal with this potential problem when propensity score weights are used in the estimation of the treatment effects, in this paper we propose a bootstrap bias correction estimator for the average treatment effect (ATE) obtained with the inverse propensity score (BBC-IPS) estimator. We show in simulations that the BBC-IPC performs well when we have misspecifications of the propensity score (PS) due to: omitted variables (ignorability property may not be satisfied), overlap (imbalances in distribution between treatment and control groups) and confounding effects between observables and unobservables (endogeneity). Further refinements in bias reductions of the ATE estimates in smaller samples are attained by iterating the BBC-IPS estimator.