Bury started in Horní Mísečky for the first time in the Slavic Cup in December 2012 and finished 78th over 10 km classic and 62nd place over 15 km freestyle. At the Nordic Junior World Ski Championships in 2015 in Almaty , he came in 55th place in sprint, 41st place over 10 km freestyle and 34th place in skiathlon . In the following year he won at the U23 World Championships in Râşnov 64th place over 15 km classic, 45th place over 15 km freestyle and 40th place in the sprint. At the 2017 U23 World Championships in Soldier Hollow , he finished 34th in the skiathlon, 31st place over 15 km freestyle and 11th place in the sprint. In February 2017 he completed his first World Cup race in Otepää , which he finished in 69th place in the sprint. In the 2017/18 season he reached fifth place overall in the Slavic Cup with two wins. At the U23 World Championships 2018 in Goms he came in 58th place over 15 km classic and 14th place in the sprint. In February 2018 he ran at the Olympic Winter Games in Pyeongchang on 78th place over 15 km freestyle and 30th place in sprint. At the Nordic World Ski Championships 2019 in Seefeld in Tirol , he ran on 69th place over 15 km classic, 66th place in the skiathlon and 62nd place in the sprint. After finishing 65th in the Ruka Triple at the beginning of the 2019/20 season, he scored his first World Cup points in the Tour de Ski 2019/20 , which he finished in 42nd place, with 27th place in the sprint in Val di Fiemme . This was followed by third place at the Slavic Cup in Štrbské Pleso over 15 km classic and first place in the sprint and at the end of the season eighth place in the overall ranking of the Slavic Cup