Person re-identification (ReID) models are known to suffer from camera bias, where learned representations cluster according to camera viewpoints rather than identity, leading to significant performance degradation under (inter-camera) domain shifts in real-world surveillance systems when new cameras are added to camera networks. State-of-the-art test-time adaptation (TTA) methods, largely designed for classification tasks, rely on classification entropy-based objectives that fail to generalize well to ReID, thus making them unsuitable for tackling camera bias. In this paper, we introduce DART$^3$, a TTA framework specifically designed to mitigate camera-induced domain shifts in person ReID. DART$^3$ (Distance-Aware Retrieval Tuning at Test Time) leverages a distance-based objective that aligns better with image retrieval tasks like ReID by exploiting the correlation between nearest-neighbor distance and prediction error. Unlike prior ReID-specific domain adaptation methods, DART$^3$ requires no source data, architectural modifications, or retraining, and can be deployed in both fully black-box and hybrid settings. Empirical evaluations on multiple ReID benchmarks indicate that DART$^3$ and DART$^3$ LITE, a lightweight alternative to the approach, consistently outperforms state-of-the-art TTA baselines, making for a viable option to online learning to mitigate the adverse effects of camera bias.