Traditional bridge monitoring and damage identification techniques typically rely on full-bridge coverage of sensors, such as displacement or strain sensors. However, this approach proves economically unfeasible for the vast numbers of small- and medium-span continuous beam bridges. In response to the need for rapid damage identification and integrity assessment of continuous beam bridges, a novel bridge safety monitoring method relying solely on bearing reaction forces is proposed. Firstly, the analytical expressions for the bearing reaction influence lines of a three-span continuous beam bridge under damage conditions were derived. Secondly, a rapid structural damage localization method based on the bearing reaction influence lines was proposed. Finally, feasibility and applicability were confirmed through numerical simulations and experimental validation. Additionally, the discussion includes the implementation of the warning classification and threshold setting using data from bearing force monitoring. The research demonstrates that utilizing a limited amount of bearing reaction force information can not only identify damage areas in a “non-full-coverage” manner, but also facilitates early warning and the integrity assessment of bridges. In the future, there is potential for large-scale application in medium- and small-span continuous beam bridges.