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In an era marked by an abundance of news sources, access to information significantly influences public opinion. Notably, the bias of news sources often serves as an indicator of individuals' political leanings. This study explores this hypothesis by examining the news sharing behavior of politically active social media users, whose political ideologies were identified in a previous study. Using correspondence analysis, we estimate the Media Sharing Index (MSI), a measure that captures bias in media outlets and user preferences within a hidden space. During Argentina’s 2019 election on Twitter, we observed distinct patterns of media sharing: center-right individuals predominantly shared media from center-right biased outlets, while center-left users exhibited more diverse media consumption, a significant finding in the context of political polarization. Although these results are specific to Argentina, the methodology can be applied in other countries to assess the correlation between users' political leanings and the media they share. In this work, we also explore additional metrics to quantify user bias when sharing content on social networks.