In 2009, Bevin rode for the New Zealand Bici Vida team. During this time, he won two stage victories in the 2009 Tour of Southland and victory in the Oceania Cycling Championships road race. He was the Bike New Zealand Junior Road Cyclist of the Year. Bevin then moved to the United States and briefly raced for the Rubicon–Orbea development team, with significant success, and was noticed by Bissell, an American Continental-level team. Bevin rode for Bissell until the team ended at the end of the 2013 season. During this time, he won several criterium races and victory in the 2012 Bucks County Classic. Throughout the 2014 season, he rode for the Australian team Search2retain-Health.com.au, winning the National Capital Tour and earning himself a contract with for 2015. In 2014, he also rode for the New Zealand national team at the 2014 An Post Rás, where he won two stages and the points competition and briefly led the general classification. In 2015, now riding for Avanti, Bevin came third in the New Zealand National Time Trial Championships and sixth in the New Zealand National Road Race Championships. After finishing 13th in the Cadel Evans Great Ocean Road Race, he rode in the 2015 Herald Sun Tour. In this race, he finished in the top 10 in three stages, including victory on the final stage at Arthur's Seat. He came second overall in the race, 11 seconds behind Cameron Meyer. His next race was The REV Classic in New Zealand, Bevin's home race and newly promoted to 1.2 status; Bevin won the race in a three-man sprint. Bevin then travelled to Taiwan to compete in the 2.1-ranked 2015 Tour de Taiwan. In the second stage, he won the hill-top finish ahead of Hossein Askari and took the race lead. After losing the lead to Samad Pourseyedi the following day, Bevin finished fourth overall and won the points classification, having finished in the top ten in four of the five stages. His next professional race was the Tour de Korea. Bevin finished first on stage 4 and second on five others. He also finished second in both the general and the points classifications. In August 2015, it was announced that Bevin had signed a two-year contract to ride in the UCI World Tour for, with Jonathan Vaughters describing him as "a rider who seems to have it all". He was named in the startlist for the 2016 Vuelta a España. In June 2017, he was named in the startlist for the 2017 Tour de France.
