Proactive search in conversations (PSC) aims to reduce user effort in formulating explicit queries by proactively retrieving useful relevant information given conversational context. Previous work in PSC either directly uses this context as input to off-the-shelf ad-hoc retrievers or further fine-tunes them on PSC data. However, ad-hoc retrievers are pre-trained on short and concise queries, while the PSC input is longer and noisier. This input mismatch between ad-hoc search and PSC limits retrieval quality. While fine-tuning on PSC data helps, its benefits remain constrained by this input gap. In this work, we propose Conv2Query, a novel conversation-to-query framework that adapts ad-hoc retrievers to PSC by bridging the input gap between ad-hoc search and PSC. Conv2Query maps conversational context into ad-hoc queries, which can either be used as input for off-the-shelf ad-hoc retrievers or for further fine-tuning on PSC data. Extensive experiments on two PSC datasets show that Conv2Query significantly improves ad-hoc retrievers' performance, both when used directly and after fine-tuning on PSC.