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Bearings are massively utilized in industries of nowadays due to their huge importance. Nevertheless, their defects can heavily affect the machines performance. Therefore, many researchers are working on bearing fault detection and classification; however, most of the works are carried out under constant speed conditions, while bearings usually operate under varying speed conditions making the task more challenging. In this paper, we propose a new method for bearing condition monitoring under time-varying speed that is able to detect the fault efficiently from the vibration signatures. First, the vibration signal is processed with the Empirical Wavelet Transform to extract the AM-FM modes. Next, time domain features are calculated from each mode. Then, the features' set is reduced using the Cultural Clan-based optimization algorithm by removing the redundant and unimportant parameters that may mislead the classification. Finally, an ensemble learning algorithm "Random Forest" is used to train a model able to classify the fault based on the selected features. The proposed method was tested on a time-varying real dataset consisting of three different bearing health states: healthy, outer race defect, and inner race defect. The obtained results indicate the ability of our proposed method to handle the speed variability issue in bearing fault detection with high efficiency. [ABSTRACT FROM AUTHOR]