Popularity of social media has increased rapidly and now it is very easy to interact with different persons across social media. As a result, cyberbullying towards people across social media has also increased. As cyberbullying can cause significant emotional and psychological distress, it should be detected and prevented. A lot of work has been done by researchers for cyberbullying detection in several languages except Bangla and Romanized Bangla. Therefore, we developed a model to detect cyberbullying from Bangla and Romanized Bangla texts using Machine Learning and Deep Learning algorithms. We also presented a comparative analysis among the algorithms in terms of accuracy, precision, recall, f1score and roc area. We prepared three datasets for Bangla, Romanized Bangla and combination of both from social media. The three datasets contained 5000 Bangla, 7000 Romanized Bangla and a combination of 12000 Bangla and Romanized Bangla texts. The preprocessed datasets were trained using the Machine Learning and Deep Learning algorithms and the model performances were evaluated to present the comparative analysis. Deep Learning algorithm CNN performed best for the Bangla Dataset by achieving 84% accuracy. For the other two datasets Machine Learning algorithm Multinomial Naïve Bayes performed best by achieving 84% accuracy in Romanized Bangla dataset and 80% accuracy in the combined dataset.