Energy conservation is crucial in Wireless Sensor Networks (WSNs) for prolonging sensor node's life. This research attempts to gain benefits of Bayesian classifier through development of a Bayesian Classifier-Based Energy Aware Routing algorithm (BBEAR) for mobile WSNs. Through implementing a Bayesian classifier for routing process, a superior routing algorithm is designed with an intelligent node message rebroadcast decision. This paper discusses the proposed algorithm design and presents a comparison of its performance with flooding technique. BBEAR workflow is described, along with its classifier mechanism that allows the message routing judgment by each sensor node to be based on several node's and message's classifying attributes. In contrast to other routing schemes developed for WSN, BBEAR algorithm incorporates several node attributes, including: remaining energy that the nodes have, distance to the sink, number of messages being queued, node's success rate, delay of the received message, as well as the number of message duplicates received by the node. The BBEAR performance is also discussed and evaluated in terms of various measures such as: throughput, number of duplicates received, average delay, and the lifetime of the nodes. The simulation study of the proposed algorithm shows its superiority over flooding: as it provides 15% gain in message throughput, four times reduction of duplicates, and gives an extension of 60% nodes' lifetime while still maintaining the delay and delay jitter at low levels.