Bayesian optimization (BO) is a promising strategy for accelerating gradient-elution liquid chromatography (LC) method development, but its practical success depends on several tightly coupled components. Here we report two main advances. First, for the Gaussian process (GP) surrogate models used within BO, we introduce a shape-aware gradient representation that compares gradient profiles directly through a Wasserstein-distance kernel, rather than through the pump-timetable coordinates used by standard representations. Second, we establish a robust automated acquisition and analysis workflow based on a trap phase that isolates gradient-driven elution and makes reliable closed-loop measurement possible. These are supported by three refinements: a flexible gradient domain with variable method duration and user-defined composition bounds, a window-relative sampler for monotonic gradient programs, and an adaptive reference point for multi-objective optimization. Across in silico and experimental datasets, Wasserstein-based representations generally predict separation quality more accurately than timetable-based approaches, especially when only a few training samples are available. This improved accuracy translates into more data-efficient singleand multi-objective optimization campaigns. Finally, we demonstrate the closed-loop framework in experimental case studies, where both single-and multi-objective campaigns improve upon a custom baseline method for a polymer-additive sample. Together, these results show that shape-aware gradient representations improve both GP predictive accuracy and BO sample efficiency, and that a flexible gradient domain, robust automated acquisition and analysis, and compatible sampling and optimization strategies enable effective closed-loop LC method development