Achieving diverse and high-quality audio transformations from text prompts remains challenging, as existing methods are fundamentally constrained by their reliance on a limited set of differentiable audio effects. This paper proposes FxSearcher, a novel gradient-free framework that discovers the optimal configuration of audio effects (FX) to transform a source signal according to a text prompt. Our method employs Bayesian Optimization and CLAP-based score function to perform this search efficiently. Furthermore, a guiding prompt is introduced to prevent undesirable artifacts and enhance human preference. To objectively evaluate our method, we propose an AI-based evaluation framework. The results demonstrate that the highest scores achieved by our method on these metrics align closely with human preferences. Demos are available at https://hojoonki.github.io/FxSearcher/