Reasoning traces improve vision-language models on complex multimodal tasks, but forcing every input to follow a long reasoning process leads to overthinking and unnecessary inference cost. We study adaptive fast/slow thinking for VLMs, where one model answers directly for simple inputs and reasons step by step when needed. Fast answers and slow traces often come from distinct behavior policies, making a single-reference offline objective misweight one mode. We propose DUAL-REFERENCE BOLT (DR-BOLT), which distinguishes the desired fast/slow mixture reference from the sampling distribution and corrects their mismatch in reward-weighted training. Fast/slow partition competition explains routing in the optimal target; an efficient source-wise correction approximates the exact objective when response formats are well separated. Matched Qwen3-VL comparisons use identical candidate banks to isolate the objective from slow-teacher quality. DR-BOLT improves score-length trade-offs over the evaluated offline and online baselines on ScienceQA and three held-out transfer benchmarks, with a 24.1% cross-benchmark slow ratio and a 2.90-fold end-to-end training speedup over reproduced GRPO. These results support adaptive reasoning in the studied two-reference setting, while broader robustness remains open. Our code is available at https://github.com/HongbinLin3589/DR-BOLT.

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