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This paper proposes an AI-based sensory glove system aimed at recognizing Bengali sign language (BaSL) in order to assist the Bengali speech disabled community to overcome the communication barrier. In the proposed design, several sensors such as flex, accelerometer, and gyroscopes were embedded in a hand glove worn by a speech-disabled person to capture the signals generated from the gestures. Two different architectures were proposed to identify the corresponding Bengali word from Bengali sign, one based solely on a convolutional neural network (CNN), and the other - a combination of CNN and long short-term memory (LSTM) network. From the experiment results of the prototype on sign samples related to 41 different Bengali words, it was observed that the average recognition accuracy of the prototype incorporated with CNN and LSTM based architecture was 94.73%, while it is 90.34% for the prototype with CNN based architecture. Experiment results also demonstrated user independent features of the sensory glove system. Moreover, analysis of the performance of the AI-based sensory glove system in terms of latency, user comfort, and battery backup revealed its competitive features compared to other commercially available devices.