This paper is devoted to thoroughly investigating how to bootstrap the ROC curve, a widely used visual tool for evaluating the accuracy of test/scoring statistics in the bipartite setup. The issue of confidence bands for the ROC curve is considered and a resampling procedure based on a smooth version of the empirical distribution called the "smoothed bootstrap" is introduced. Theoretical arguments and simulation results are presented to show that the "smoothed bootstrap" is preferable to a "naive" bootstrap in order to construct accurate confidence bands.