Before his career as an indoor volleyball player, Bartman played beach volleyball with Michał Kubiak. They won a gold medal at the European U-18 Championship in 2004 and a silver medal at the World U-18 Championship, also in 2004. Both Kubiak and Bartman gave up playing beach volleyball.
Bartman debuted in PlusLiga in the club MOS Wola Warszawa during a match against Skra Bełchatów in 2003. In 2013/2014, he played for Italian club Casa Modena. With the Italian team,he played in the semifinals of the Italian Championship, but lost in matches against Lube Banca Macerata. On July 2014, Bartman announced he would be returning to Polish club, Jastrzębski Węgiel, where he played in the 2012/2013 season. His team took 4th place in 2014–15 PlusLiga. On June 19, 2015 he announced that he moved to Chinese team Sichuan Chengdu, together with Michal Lasko - one of his team mates from previous club.