Bush, who starred on Chicago P.D. from 2014 to 2017, was married to One Tree Hill costar Chad Michael Murray from April 2005 to December 2006. After relationships with James Lafferty, Austin Nichols, Dan Fredinburg and Soffer, she began dating Grant Hughes in 2020. The pair announced their engagement in August 2021. Bush and Hughes got married at Philbrook Art Museum in Tulsa County, Oklahoma, on June 11, 2022.
Us confirmed in August 2023 that Bush filed for divorce from Hughes after 13 months of marriage. She started sparking romance rumors with soccer star Ashlyn Harris in October 2023. Bush confirmed their relationship in April 2024, when she came out as queer in a Glamour cover story.