Cyberbullying (CB) has become increasingly prevalent in social media platforms. With the popularity and widespread use of social media by individuals of all ages, it is vital to make social media platforms safer from cyberbullying. This paper presents a hybrid deep learning model, called DEA-RNN, to detect CB on Twitter social media network. The proposed DEA-RNN model combines Elman type Recurrent Neural Networks (RNN) with an optimized Dolphin Echolocation Algorithm (DEA) for finetuning the Elman RNN's parameters and reducing training time. We evaluated DEA-RNN thoroughly utilizing a dataset of 10000 tweets and compared its performance to those of state-of-the-art algorithms such as Bi-directional long short term memory (Bi-LSTM), RNN, SVM, Multinomial Naive Bayes (MNB), Random Forests (RF). The experimental results show that DEA-RNN was found to be superior in all the scenarios. It outperformed the considered existing approaches in detecting CB on Twitter platform. DEA-RNN was more efficient in scenario 3, where it has achieved an average of 90.45% accuracy, 89.52% precision, 88.98% recall, 89.25% F1-score, and 90.94% specificity.