Vector or numeric representation of text documents has been a revolution in natural language processing as it represents similar parts of text in such a way that they are very close to each other, making it very easy to classify or find similarities among them. These vectors also represent the way we use the words or parts of documents as well which helps finding similarity even between pair of words. While word2vec is such a technique that represents each word as a vector, doc2vec takes it to another level by representing a whole sentence or document as a vector. Being able to represent an entire document as a vector allows comparing a substantial number of words or sentences at a time which can save computational power as well as bandwidth. This relatively newer doc2vec technology has not yet been implemented for Bengali sentiment analysis and its feasibility is also unknown. In this study, we have trained a doc2vec model using a corpus constructed with 7,000 Bengali sentences. The model consists of two types of data differentiated by their polarity i.e. positive and negative. Later, we have employed several machine learning algorithms for comparing the accuracy of classification among which Bi-Directional Long Short-Term Memory (BLSTM) has obtained the highest accuracy of 77.85% along with precision, recall and F-1 score of 78.06%,77.39% and 77.72% respectively.