Large language models (LLMs) are often queried multiple times at test time, with predictions aggregated by majority vote. While effective, this self-consistency (Wang et al., 2023) strategy requires a fixed number of calls and fails when the correct answer is infrequent. We introduce Confidence-Guided Early Stopping (CGES), a Bayesian framework that forms posteriors over candidate answers and adaptively halts sampling once one answer accumulates enough posterior mass. We prove guarantees in both an ideal calibrated regime and a realistic noisy-confidence regime under a directional drift condition. Averaged over five reasoning benchmarks, CGES reduces the average number of calls by 58% on average (from 16.0 to 6.7) while matching its accuracy within 0.4 percentage points of self-consistency.