Remaining useful life (RUL) estimation of Lithium-ion batteries (LIBs) is essential to assess their long-term reliability. RUL can enable the prediction of LIB failure and thereby can mitigate operational risk. Machine deep-learning (MDL) models are popularly being trained on historical LIB capacity discharge data for RUL predictions by many research groups. Out of the variety of MDL methods, the Recurrent neural network (RNN) is being widely used to analyze LIB capacity discharge data; nevertheless, RNN is inadequate in learning the long-term dependencies, which limits its usage for the prediction of RUL. Therefore, this work investigates Recurrent Neural Network (Bidirectional Long Short-Term Memory) RNN (Bi-LSTMs) for the prediction of RUL. Here, RNN with forward and backward long short-term memory (Bi-LSTMs) is applied to realize both forward and backward long-term dependencies of LIB capacity discharge data and then construct a discharge capacity-based RUL predictor. Raw, unaltered (to capture intricacies, and variations in real-world data) multiple LIBs capacity discharge data are deployed for RNN (Bi-LSTMs) training and validation. Further, optimal hyperparameters for RNN (Bi-LSTMs) are obtained through Bayesian optimization. Optuna, an open-source Python library, is used for hyperparameter optimization using a hyperparameter search space. Therefore, the whole training process is automated with only inputs required including LIB capacity discharge data and hyperparameters search space. As no manual entry of hyperparameters is required, the model has the ability to be trained with any available LIB capacity discharge data. Furthermore, the RNN (Bi-LSTMs) demonstrated competency in predicting capacity discharge characteristics and provided good estimations of the RUL with %error in predicted RUL with respect to the experimental true RUL as low as 14.3%.