Rolling element bearings are among the most critical components in rotating machinery. Bearing faults can lead to significant machine failures and hence demand efficient strategies for condition monitoring and fault diagnosis. Although machine learning (ML)-based condition monitoring is widely prevalent, in many scenarios the ML models perform poorly due to feature redundancy and lack of proper hyperparameter tuning. This work presents a hybrid ML model for the fault diagnosis of bearings by combining the long short-term memory (LSTM) networks with the support vector machine (SVM) classifier. Time domain and frequency domain features are extracted from the raw vibration signals, which are then processed by a dual-layer LSTM network. The output features from the LSTM model are fed into the Bayesian-optimized SVM classifier. The proposed hybrid technique gave superior classification performance and produced a multi-fault classification accuracy of 99%.