Bearing is a key component in rotary machines. Their failures may cause the abrupt shutdown of these machines, which would result in substantial economic losses. Therefore, the prediction of the remaining useful life (RUL) of bearings is regarded as one of the critical approaches to avoid failure of bearings and their systems. In this article, an ensemble data-driven approach is proposed to predict the RUL of bearings. It uses feature extraction, an attention mechanism, and uncertainty analysis. First, the features embedded in the bearings' vibration signals are extracted. Second, a stacked gated recurrent unit (GRU) is constructed to predict the bearing RUL. A novel attention mechanism based on dynamic time warping (DTW) is developed to improve the performance of information extraction, and a Bayesian approach is employed to analyze the prediction uncertainty. Finally, the proposed approach is validated using two benchmark-bearing data sets. The results show that the proposed approach can predict the bearing RUL effectively, and the prediction uncertainty can also be evaluated.