This study presents a Bayesian Optimisation (BO) framework for the mass minimisation of variable-stiffness (VS) composite cylinders under multiple buckling constraints, incorporating manufacturing limitations derived from filament winding processes. A computationally efficient single-curvature finite element model is used to evaluate the linear buckling response of multilayered shells. BO simultaneously optimises fibre paths, number of layers, and thickness distribution, achieving comparable or improved performance relative to a Genetic Algorithm (GA) while reducing simulation time by up to 70 %. Across most design loads, BO delivers structurally efficient solutions with smooth thickness transitions and local stiffness tailoring. Although GA outperformed BO in the highest load case in terms of weight and buckling capacity, BO retained competitive performance and demonstrated higher modal richness. Buckling mode analyses revealed that BO designs support mixed-mode instabilities with greater circumferential complexity, enhancing structural adaptability. In contrast, GA designs exhibited more uniform fibre paths and axial-dominated modes, reflecting conservative reinforcement strategies. These findings highlight the capability of BO to exploit complex design spaces more effectively, offering a scalable and data-efficient alternative to traditional optimisation methods. The proposed framework is particularly well suited for high-fidelity, simulation-driven design of advanced composite structures where computational cost and manufacturability are critical constraints.