The performance of automatic speech recognition (ASR) systems typically degrades significantly when the training and test data domains are mismatched. In this paper, we show that self-training (ST) combined with an uncertainty-based pseudo-label filtering approach can be effectively used for domain adaptation. We propose DUST, a dropout-based uncertainty-driven self-training technique which uses agreement between multiple predictions of an ASR system obtained for different dropout settings to measure the model's uncertainty about its prediction. DUST excludes pseudo-labeled data with high uncertainties from the training, which leads to substantially improved ASR results compared to ST without filtering, and accelerates the training time due to a reduced training data set. Domain adaptation experiments using WSJ as a source domain and TED-LIUM 3 as well as SWITCHBOARD as the target domains show that up to 80% of the performance of a system trained on ground-truth data can be recovered.