His first outing at national level was in 2010, when he was a Kenyan junior finalist. He made his breakthrough nationally at senior level with a run of 50.39 seconds to place third at the Kenyan Athletics Championships in 2011. He missed most of the 2012 season but returned in 2013 with runner-up finishes at both the national championships and world trials. A new personal best of 49.70 seconds at the latter meet placed him 53rd globally for the season.
Another runner-up finish at the national level earned him selection for both the 2014 Commonwealth Games and the 2014 African Championships in Athletics. At the Commonwealth Games he failed to make the 400 m hurdles final and was also eliminated in the heats of the 4 × 400 m relay after Kenya were disqualified. At the African Championships in Athletics, he won a bronze medal in the 400 m hurdles, achieving a new personal best of 49.03 seconds, and a bronze medal in the 4 × 400 m relay with teammates Mark Mutai,
Solomon Buoga and Boniface Mucheru.
Bett began to compete on the international track and field circuit in 2015 and had wins at the
Savo Games and
Lappeenranta Games in Finland. A personal best of 48.29 seconds at the 2015 Athletics Kenya World Championship Trials brought him selection for the national team and raised him to third on the global rankings. At the
2015 World Athletics Championship in Beijing, Bett achieved his biggest result, winning the 400 metres hurdles event with a time of 47.79 seconds. Bett's win was Kenya's first in the history of the World Championships, for an event shorter than 800 metres. Bett's Beijing run was the fastest time for the distance in the whole of the 2015 season.
Bett had a poor start to the 2016 season, with a season's best time of 49.31 going into the 2016 Olympic Games in Rio de Janeiro. However, Bett was still considered one of the favourites for the 400 metres hurdles event, following his 2015 World Championships win. However, he made a mistake in the preliminary round when he tripped over the 10th and final hurdle whilst in second place. He eventually finished last in the heat, but was disqualified anyway, and failed to reach the semifinal.