State of charge (SoC) estimation is critical for the effective functioning of battery management systems in electric vehicles. Despite significant advancements in SoC estimation for lithium-ion batteries, existing methods still face challenges in accurately estimating the SoC under dynamic operating conditions, especially in the presence of system nonlinearities like temperature fluctuations, load variations, and aging effects. This work presents a closed-loop SoC estimation framework that integrates a Bidirectional Long Short-Term Memory (Bi-LSTM) neural network with a covariance correction extended Kalman filter (CCEKF), termed as Bi-LSTM-CCEKF, to enhance the accuracy and robustness of SoC prediction. The second-order equivalent circuit battery model is developed, and its parameters are identified using the cuckoo search algorithm. The proposed system utilizes a Bi-LSTM-CCEKF to compensate for the final SoC prediction and dynamically adjust the covariance matrices in the extended Kalman filter, resulting in covariance and error correction based on real-time data. The proposed approach is evaluated with different error matrices that show optimal performance than the existing methods. The system is validated with experimental data, demonstrating significant improvements in SoC estimation accuracy and robustness under various testing profiles. The Bi-LSTM-CCEKF method has a wide operating condition adaptability for electric vehicle battery management system applications.