Multi-vector late-interaction retrievers such as ColBERT achieve state-of-the-art quality, but their query-time cost is dominated by exhaustively computing token-level MaxSim interactions for every candidate document. The MaxSim scores of $N$ candidates against $T$ query tokens form an $N\times T$ matrix whose row-sums are the late-interaction scores, and identifying the top-$K$ rarely requires every entry. We introduce Col-Bandit, a query-time estimator of the exhaustive-MaxSim top-$K$: it reveals matrix entries in batches, maintains a finite-population Bernstein-Serfling confidence interval on each candidate's score, and permanently drops any document whose upper bound falls below the $K$-th largest lower bound, computing only the cells needed to separate the top-$K$. A single relaxation knob $α_{\mathrm{ef}}\in(0,1]$ tunes the compute-fidelity trade-off. We deploy $α_{\mathrm{ef}}{=}0.2$, while $α_{\mathrm{ef}}{=}1$ admits a $δ$-PAC guarantee under a simplified radius. On BEIR and REAL-MM-RAG, Col-Bandit preserves $\geq 90\%$ fidelity to the exhaustive top-$5$ on every corpus while cutting MaxSim FLOPs by up to ${\sim}8\times$, for up to ${\sim}13\times$ single-thread CPU speedups across x86 and ARM. A drop-in reranking layer, it needs no retraining or index changes.

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