Social media, a vast platform for communication and entertainment, unfortunately, is an ideal breeding ground for cyberbullying. While most common among teenagers, it also affects other demographics. Despite strict zero-tolerance policies on social media, the elusive nature of cyberbullying persists. Simple word searches are insufficient, leading to the exploration of Natural Language Processing (NLP) to detect and classify cyberbullying. This study balances result accuracy with model simplicity, crucial for an effective detector. Quick identification of offensive content is essential to combat cyberbullying. The ever-changing slang and trends require an easily updatable detector. Using a cyberbullying dataset from real tweets on X (formerly Twitter), this study initially applies traditional machine learning algorithms, including Logistic Regression, Support Vector Machines, Decision Trees, and Random Forests. The investigation then moves to Transformers-based autoencoders from the BERT family, including sentence-transformers. However, these models require significant memory and disk space due to their large number of training parameters. The study focuses on the efficiency of cyberbullying detectors using character-level language models based on the bidirectional long-short-term memory (BiLSTM) neural architecture. Our experiments demonstrate that these detectors offer comparable performance and provide a practical option for real-world deployment.