Fibre composites, and especially aligned discontinuous composites (ADCs), offer enormous versatility in composition, microstructure, and performance, but are difficult to optimise, due to their inherent variability and myriad permutations of microstructural design variables. This work combines an accurate yet efficient virtual testing framework (VTF) with a data-driven intelligent Bayesian optimisation routine, to maximise the mechanical performance of ADCs for a number of single- and multi-objective design cases. The use of a surrogate model helps to minimise the number of optimisation iterations, and provides a more accurate insight into the expected performance of materials which feature significant variability. Results from the single-objective optimisation study show that a wide range of structural properties can be achieved using ADCs, with a maximum stiffness of 505 GPa, maximum ultimate strain of 3.94%, or a maximum ultimate strength of 1.92 GPa all possible. A moderate trade-off in performance can be achieved when considering multi-objective optimisation design cases, such as an optimal ultimate strength & ultimate strain combination of 982 MPa and 3.27%, or an optimal combination of 720 MPa yield strength & 1.91% pseudo-ductile strain.