Bence Pásztor has competed in hammer throw competitions since 2009. One year later, with a casting weight of 5 kilograms, he already threw a distance of 75.52 m. His achievements brought him top places in national adult championships at a young age. In July 2011 he competed at the U18 World Championships in Lille, where he won the gold medal with a width of 82.60 m. Only a few days later he also won the European Youth Olympic Festival in Trabzon with a personal best of 84.41 m. From the 2012 season he entered the U20 age group with a casting weight of 6 kilograms. In July he won the silver medal at the U20 World Championships in Barcelona. He then became the Hungarian U18 champion.
From 2013 he then focused entirely on the hammer throw, after having also competed regionally in the shot put and discus throw until the previous year. In June he won gold at the national U20 championships and then started a month later at the U20 European championships in Rieti. In the final of the championships he set a new record with 77.35 m with a casting weight of 6 kilograms, with which he won the silver medal. In May 2014 he threw over 80 meters for the first time at the throwing days in Halle . In the summer, like two years before, he again won silver at the U20 World Championships . As in 2012, he only had to admit defeat to Ashraf Amgad el-Seify from Qatar . At the beginning of the 2016 season, Pásztor will start with the final casting weight of 7.26 kilograms. In June he set his season best of 75.74 m. A month later he won the bronze medal at the U23 European Championships in Tallinn. In August he was the Hungarian runner-up in the same month in which he first competed in an international championship among adults at the World Championships in Beijing. With 71.14 m, however, he retired, far behind, in the qualification. A year later he was eliminated from the European Championships in Amsterdam. After 8th place in his qualification group, he finished 17th overall.
In 2017, Pásztor took part in the U23 European Championships for the last time , this time in Bydgoszcz. In the final he reached 71.51 m and thus won the silver medal behind his compatriot Bence Halász . In 2018 he was eliminated from qualification at the European Championships in Berlin and ended up in 26th place.