Sentiment analysis is the research area that deals with analysis of sentiments expressed in the social media texts written by the internet users. Sentiments of the users are expressed in various forms such as feelings, emotions and opinions. Tweet sentiment polarity detection is an important sentiment analysis task which is to classify an input tweet as one of three classes: positive, negative and neutral. In this study, we compare various deep learning methods that use LSTM, BILSTM and CNN for the sentiment polarity classification of Bengali tweets. We also present in this paper a comparative study on the Bengali tweet sentiment polarity classification performances of the traditional machine learning methods and the deep learning methods.