Energy-structure-function (ESF) maps have emerged as a powerful tool for in silico materials design, coupling crystal structure prediction techniques with property simulations to assess the potential for new candidate materials to display desirable properties. Despite continuing increases to accessible computational power, however, the computational cost of acquiring an ESF map often remains too high to allow integration into true high-throughput virtual screening techniques. In this paper, we propose the next evolution of the ESF map, which uses parallel Bayesian optimization to selectively acquire energy and property data, generating the same levels of insight at a fraction of the computational cost by limiting the expensive property calculations to a small fraction of the predicted crystal structures associated with a molecule. We utilize this approach to obtain a two orders of magnitude speedup on a previous ESF study that focused on methane capture materials, saving over 500,000 CPUh from the original protocol. Through acceleration of the acquisition of ESF-type insight, we pave the way for the use of ESF maps in automated ultra-high throughput screening pipelines. This greatly reduce the opportunity risk associated with the choice of system to calculate. For example, it will allow researchers to use ESF maps in the search for physical properties where the computational costs are currently just intractable, or to investigate orders of magnitude more systems for a given computational cost.