Expensive black-box optimization spends its budget fast. Simulation-driven engineering design and hyperparameter tuning admit only a few hundred true function evaluations, so every observation collected during the search becomes a priced asset. This paper deploys GAS-Bacterial Foraging Optimization (BFO), a surrogate-assisted optimizer in which a swarm of thirty large-language-model-mediated bacterial agents runs chemotaxis over a shared collective memory. Agents post structured textual observations of their local landscape throughout the run, and every ten iterations a language model condenses this memory into a natural-language pheromone, a small set of weighted region summaries that defines an explicit chemoattractant field biasing every agent's movement; a hallucination guard cross-checks each directional cue against the surrogate gradient and falls back to a classical tumble on disagreement. The evaluation rebuilds the budget ledger from the ground up: Twelve problems, ten mathematical benchmarks and two simulated engineering cases, three budget tiers of 150, 400, and 900 true evaluations, thirty runs per cell, and fourteen methods, nine established references plus four language-model optimizers newly admitted to the race, OPRO, FunSearch, EoH, and ReEvo, raced under token-matched accounting. Survival analysis on tier-relative time-to-target carries the inference: GAS-BFO holds the best mean gap on 22 of 36 problem-tier cells, reaches the target gap with the highest probability at every tier, and is significantly faster than all thirteen rivals at the 400- and 900-evaluation tiers under Holm-corrected log-rank tests, with hazard ratios pricing the separation, while conceding specific cells, the mixed-space tuning task to Tree-structured Parzen Estimation (TPE) among them, that the ledger records openly. Ablations attribute the gain to generative condensation and collective memory; the token tables state the price, one to three dollars per run at deployment tiers; and under bursty message dropout and controlled distributional shift the swarm amortizes knowledge where single-model and single-history rivals concentrate it, retaining 79.4% of lossless quality at a 60% loss rate against 41.2% for Bayesian Optimization with Expected Improvement (BO-EI).