In the era towards green aviation, efficient flight operations and environmental sustainability are paramount concerns for airlines. In day-to-day operations, this can be achieved by flying aircraft in favourable wind conditions to reduce economic cost and environmental impact. This paper presents a bi-level aircraft trajectory optimisation algorithm designed for operations in unsteady wind conditions. The algorithm begins with a modified Dijkstra approach applied to a coarse grid, providing a globally optimised solution in the low-fidelity space. This is followed by high-fidelity optimisation using shape optimisation principles with free-form deformation. By reformulating the problem as a shape optimisation, the constrained optimisation is converted into an unconstrained one with fewer variables, thereby substantially reducing the computational cost. The bi-level approach accelerates convergence and minimises the risk of local minima. Applied to 2435 flights operated by our airline partner in 2022, the algorithm demonstrated average travel time reductions of 13.1%, 1.7%, and 1.2% for routes between Hong Kong and London, Sydney, and Singapore, respectively. The method is shown to be especially effective for east-west flights in the presence of jet streams. With GPU acceleration and CPU multiprocessing, the algorithm enables real-time trajectory optimisation, offering notable potential benefits in terms of sustainability, passenger comfort, and operational efficiency.