We develop a flexible content-based search model that links the content preferences of search engine users to query search volume and click-through rates. Content preferences are defined over latent topics that describe the content of search queries and search result descriptions. Moreover, our model allows content preferences to vary systematically based on the context of the search. To facilitate efficient and scalable inference, we develop a full Bayesian variational inference algorithm. We evaluate our modelling framework using real-world data on searches for TV shows on the Bing search engine. We illustrate how our model can quantify the content preferences associated with each query, and how these preferences vary systematically based on whether the query is observed before, during, or after a TV show is aired. We also show that our model can help the search engine improve its ranking of search results. In addition to search engines, advertisers can apply our model to understand their search advertising campaign data and gain insights into which search ads should be targeted to which users, when, and on which devices.