We address the challenge of designing cellular networks for uncrewed aerial vehicles (UAVs) corridors through a novel data-driven approach. We assess multiple state-of-the-art high-dimensional Bayesian optimization (HD-BO) techniques to jointly optimize the cell antenna tilts and half-power beamwidth (HPBW). We find that some of these approaches achieve over 20dB gains in median SINR along UAV corridors, with negligible degradation to ground user performance. Furthermore, we explore the HD-BO's capabilities in terms of model generalization via transfer learning, where data from a previously observed scenario source is leveraged to predict the optimal solution for a new scenario target. We provide examples of scenarios where such transfer learning is successful and others where it fails. Moreover, we demonstrate that HD-BO enables multi-objective optimization, identifying optimal design trade-offs between data rates on the ground versus UAV coverage reliability. We observe that aiming to provide UAV coverage across the entire sky can lower the rates for ground users compared to setups specifically optimized for UAV corridors. Finally, we validate our approach through a case study in a real-world cellular network, where HD-BO identifies optimal and non-obvious antenna configurations that result in more than double the rates along 3D UAV corridors with negligible ground performance loss.