Wireless sensor networks (WSNs) are promising technologies for exploring harsh environments, such as oceans, wild forests, volcanic regions and outer space. Since sensor nodes may have limited transmission range, application packets may be transmitted by multi-hop communication. Thus, connectivity is a very important issue. A bridge is a critical edge whose removal breaks the connectivity of the network. Hence, it is crucial to detect bridges and take preventions. Since sensor nodes are battery-powered, services running on nodes should consume low energy. In this paper, we propose energy-efficient and distributed bridge detection algorithms for WSNs. Our algorithms run single phase and they are integrated with the Breadth-First Search (BFS) algorithm, which is a popular routing algorithm. Our first algorithm is an extended version of Milic's algorithm, which is designed to reduce the message length. Our second algorithm is novel and uses ancestral knowledge to detect bridges. We explain the operation of the algorithms, analyze their proof of correctness, message, time, space and computational complexities. To evaluate practical importance, we provide testbed experiments and extensive simulations. We show that our proposed algorithms provide less resource consumption, and the energy savings of our algorithms are up by 5.5-times.