We study the problem of visual surface inspection of a bridge for defects using an Unmanned Aerial Vehicle (UAV). We do not assume that the geometric model of the bridge is known beforehand. Our planner, termed GATSBI, plans a path in a receding horizon fashion to inspect all points on the surface of the bridge. The input to GATSBI consists of a 3D occupancy map created online with LiDAR scans. Occupied voxels corresponding to the bridge in this map are semantically segmented and used to create a bridge-only occupancy map. Inspecting a bridge voxel requires the UAV to take images from a desired viewing angle and distance. We then create a Generalized Traveling Salesperson Problem (GTSP) instance to cluster candidate viewpoints for inspecting the bridge voxels and use an off-the-shelf GTSP solver to find the optimal path for the given instance. As the algorithm sees more parts of the environment over time, it replans the path to inspect novel parts of the bridge while avoiding obstacles. We evaluate the performance of our algorithm through high-fidelity simulations conducted in AirSim and real-world experiments. We compare the performance of GATSBI with a classical exploration algorithm. Our evaluation reveals that targeting the inspection to only the segmented bridge voxels and planning carefully using a GTSP solver leads to a more efficient and thorough inspection than the baseline algorithm.