Bridges are key components of transportation networks around the world. Millions of bridges were constructed over the past centuries. However, many of these structures are aging or facing extreme events. Current inspection methods are reliant on manual labor, which only makes them costly, inefficient, and outdated. These current approaches lack a clear system for optimally inspecting the bridge, obtaining better information about its condition. To address this challenge, this paper presents a novel framework guided by Bayesian optimization for detecting bridge local damage using sensors attached to Unmanned Aerial Vehicles (UAVs). A cost-effective and practical Utility Function Framework (UFF) method is developed, which leverages orchestrated UAVs with optimum spacing. To rigorously validate the approach, a validation analysis is conducted by exhaustively testing all possible sensor placements on a 10 m bridge, providing a theoretical baseline against which the proposed method is evaluated. Additionally, a field case study validated the proposed method of sensor placement. The framework is validated as a proof-of-concept using a 10 m numerical benchmark and a field-inspired case study, and it is intended to demonstrate feasibility rather than universal performance across all bridge typologies. While the study focuses on a single span with a controlled damage scenario, the results establish feasibility and motivate future validation on longer spans, varied bridge typologies, and practical field investigations.