Dense retrievers enhance retrieval by encoding queries and documents into continuous vectors, but they often struggle with reasoning-intensive queries. Although Large Language Models (LLMs) can reformulate queries to capture complex reasoning, applying them universally incurs significant computational cost. In this work, we propose Adaptive Query Reasoning (AdaQR), a hybrid query rewriting framework. Within this framework, a Reasoner Router dynamically directs each query to either fast dense reasoning or deep LLM reasoning. The dense reasoning is achieved by the Dense Reasoner, which performs LLM-style reasoning directly in the embedding space, enabling a controllable trade-off between efficiency and accuracy. Experiments on large-scale retrieval benchmarks BRIGHT show that AdaQR reduces reasoning cost by 28% while preserving-or even improving-retrieval performance by 7%.