The Internet is currently the largest platform for global communication including expressions of opinions, reviews, contents, images, videos and so forth. Moreover, social media has now become a very broad and highly engaging platform due to its immense popularity and swift adoption trend. Increased social networking, however, also has detrimental impacts on the society leading to a range of unwanted phenomena, such as online assault, intimidation, digital bullying, criminality and trolling. Hence, cyberbullying has become a pervasive and worrying problem that poses considerable psychological and emotional harm to the people, particularly amongst the teens and the young adults. In order to lessen its negative effects and provide victims with prompt support, a great deal of research to identify cyberbullying instances at various online platforms is emerging. In comparison to other languages, Bangla (also known as Bengali) has fewer research studies in this domain. This study demonstrates a deep learning strategy for identifying cyberbullying in Bengali, using a dataset of 12282 versatile comments from multiple social media sites. In this study, a two-layer bidirectional long short-term memory (Bi-LSTM) model has been built to identify cyberbullying, using a variety of optimisers as well as 5-fold cross validation. To evaluate the functionality and efficacy of the proposed system, rigorous assessment and validation procedures have been employed throughout the project. The results of this study reveals that the proposed model's accuracy, using momentum-based stochastic gradient descent (SGD) optimiser, is 94.46%. It also reflects a higher accuracy of 95.08% and a F1 score of 95.23% using Adam optimiser as well as a better accuracy of 94.31% in 5-fold cross validation.