Bush's confirmation hearings were controversial as it was revealed that he had authored pseudonymous blog posts in which he opposed gay rights, abortion, and cited alt-right websites promoting birtherism and other false right-wing conspiracy theories.

[11][12][13] On May 8, 2017, President Donald Trump nominated Bush to the United States Court of Appeals for the Sixth Circuit seat vacated by Judge Danny Julian Boggs, who assumed senior status on February 28, 2017.

[3] His blog posts expressed opposition to gay marriage, the Affordable Care Act, public financing of political campaigns, and the idea of trying terrorists in civilian courts.

[23] Bush authored the opinion in EMW Women's Surgical Center v. Beshear (2019), in which the Sixth Circuit upheld, 2–1, a Kentucky law compelling physicians to show and describe a fetal ultrasound to patients before performing an abortion.

[27][28] Bush authored the court's opinion in McDonald v. UAW-GM Center for Human Resources[29] finding that the Americans with Disabilities Act did not require the defendant to extend the employee's lunch break for her to exercise.

[30][31] Bush joined the court's opinion in Hagy v. Demers & Adams, LLC[32] involving a letter sent from an attorney discharging the plaintiffs' debts following a mortgage foreclosure.

Despite the fact that no injury or harm came from the failure to disclose, nor was the letter unfair, deceptive, or harassing as the FDCPA aims to prevent, the district court awarded $1,000 in statutory penalties and over $74,000 in attorneys fees to the plaintiffs.

[38][39] The circuit court's unanimous decision to remand for a jury trial on unconstitutional use of force, false arrest, extended detention, and malicious prosecution claims was authored by Bush.

[40][41] In July 2020, Bush wrote for the unanimous panel when it found that the warrantless use of a camera hidden in the hallway outside the accused's apartment door was not an unconstitutional search of the home's curtilage.