Cyberbullying has become a pervasive issue on social media platforms, necessitating effective detection methods across diverse linguistic contexts. This study proposes a methodology for cyberbullying detection in Kannada, Kannada written in English, and English texts. Leveraging machine learning and natural language processing techniques, we develop and evaluate three types of models: traditional (Random Forest, Support Vector Machine), neural network (Single-Layer Perceptron, Multi-layer Perceptron), and deep neural network (Long Short-Term Memory, BERT, IndicBERT). Results show that deep learning models, particularly those leveraging pre-trained language models, exhibit superior performance in detecting offensive language, contributing to the ongoing efforts to combat cyberbullying in contemporary discourse. The model BERT outperforms the Random Forest model by 5.40 in accuracy and 13.79 in F1-score. Similarly, the Semi-Supervised model surpasses the Logistic Regression model by 10.62 in accuracy and 19.37 in F1-score, highlighting significant improvements. Additionally, an analysis of the underlying mechanisms highlights the inherent strengths of deep learning architectures, such as their ability to capture intricate linguistic patterns and contextual nuances, as well as model long-range dependencies within textual data, thereby enhancing their discriminatory capabilities in identifying cyberbullying behavior across multilingual and cross-script contexts.