Data markets serve as crucial platforms facilitating data discovery, exchange, sharing, and integration among data users and providers. However, the paramount concern of privacy has predominantly centered on protecting privacy of data owners and third parties, neglecting the challenges associated with protecting the privacy of data buyers. In this article, we address this gap by modeling the intricacies of data buyer privacy protection and investigating the delicate balance between privacy and purchase cost. Through comprehensive experimentation, our results yield valuable insights, shedding light on the efficacy and efficiency of our proposed approaches.