Watermarking has emerged as a prominent technique for LLM-generated content detection by embedding imperceptible patterns. Despite supreme performance, its robustness against adversarial attacks remains underexplored. Previous work typically considers a grey-box attack setting, where the specific type of watermark is already known. Some even necessitates knowledge about hyperparameters of the watermarking method. Such prerequisites are unattainable in real-world scenarios. Targeting at a more realistic black-box threat model with fewer assumptions, we here propose $\mathcal{B}^4$, a black-box scrubbing attack on watermarks. Specifically, we formulate the watermark scrubbing attack as a constrained optimization problem by capturing its objectives with two distributions, a Watermark Distribution and a Fidelity Distribution. This optimization problem can be approximately solved using two proxy distributions. Experimental results across 12 different settings demonstrate the superior performance of $\mathcal{B}^4$ compared with other baselines.