In 2010 Bairstow accepted a scholarship to attend the University of New Mexico. Playing sparingly his Freshman and Sophomore seasons, Bairstow saw consistent minutes in his Junior season when the Lobos won the MWC regular season and tournament championship. Bairstow had a break-out season as a senior in 2013–14. In 34 games, he averaged 20.4 points, 7.4 rebounds, 1.6 assists and 1.5 blocks per game, scoring 20 points or more in 21 games. The Lobos completed the season 27–7, giving them a combined record of 106–33 during Bairstow's four years, making his the second-winningest class ever for the program. Bairstow was named MWC Tournament MVP, Second Team All-American by Sports Illustrated, Third Team All-American by NBC Sports and CBS Sports, and Honorable Mention All-American by the Associated Press. Bairstow was honored by the MWC as academic all-conference as a senior and earned a degree in Exercise Science at UNM.

Bairstow was selected with the 49th overall pick in the 2014 NBA draft by the Chicago Bulls. On 21 July 2014, the Bulls announced they had signed Bairstow to a three-year contract, with one and a half years guaranteed. On 29 October 2014, he made his NBA debut against the New York Knicks. On 21 November, he recorded his first points as an NBA player. The Bulls advanced to the Eastern Conference Semi-finals where they lost to the Cleveland Cavaliers in 6 games. Bairstow returned to Australia to help his national team win the FIBA Oceania Championship and Qualify for the 2016 Olympic Games. On 25 July the Bulls picked up the team option for the 2015-16 season, guaranteeing his contract for the upcoming season.