In this paper, we consider a challenging scenario of localising a camera with respect to a charging station for electric buses. In this application, we face a number of problems, including a substantial scale change as the bus approaches the station, and the need to detect keypoints on a weakly textured object in a wide range of lighting and weather conditions. Therefore, we use a deep convolutional neural network to detect the features, while retaining a conventional procedure for pose estimation with 2D-to-3D associations. We leverage here the backbone of HRNet, a state-of-the-art network used for detection of feature points in human pose recognition, and we further improve the solution adding constraints that stem from the known scene geometry. We incorporate the reprojection-based geometric priors in a novel loss function for HRNet training and use the object geometry to construct sanity checks in postprocessing. Moreover, we demonstrate that our Geometry-Aware Keypoint Network yields feasible estimates of the geometric uncertainty of point features. The proposed architecture and solutions are tested on a large dataset of images and trajectories collected with a real city bus and charging station under varying environmental conditions.