2009-10: Bystrom played for the MoDo U18 and U16 teams and competed for Angermanland in the TV-Pucken tournament for high school-age players. In ten games with MoDo's U18 team he was plus-five with no points or penalties. He had an assist and was minus-four in five playoff games. In 14 Elit U18 games he had 4 goals with 6 penalty minutes. He had 1 assist in 3 games for MoDo U16 and in eight games in the TV-Pucken tournament he had 3 assists with 10 penalty minutes.
2010-11: Bystrom dressed in one game for Modo in Elitserien – spending most of the season with the club's U20 and U18 squads. Playing with his older brother Anton, a forward who was the third-leading scorer for the MoDo U20 team, he scored 1 goal with 10 assists and was plus-one with 28 penalty minutes. In six playoff games he scored 1 goal with 2 assists and was plus-one with 6 penalty minutes. In nine U18 games he scored 1 goal with 5 assists.
2011-12: Bystrom played 20 Elitserien games with MoDo and represented Sweden at the World Junior A Challenge and the 2012 U18 World Junior Championship. Averaging six minutes of ice time during his time with MODO, Bystrom had 1 assist and was +2 with 8 penalty minutes for the eighth-place club. He was scoreless in one playoff game. In 34 games for MoDo U20 he scored 7 goals with 22 assists and was plus-two with 101 penalty minutes. He had 1 goal with 3 assists and was minus-5 in eight playoff games. In four games at the World Junior A Challenge he had 1 assist. He played in six games for Sweden at the U18 WJC and was minus-one with 1 assist as the team won a silver medal. Bystrom was ranked eighth amongst European skaters in Central Scouting's final rankings prior to the 2012 NHL Draft.
A smooth skater with very good agility and recovery ability, Bystrom has good offensive tools. He’s a quality puck-mover in the transition game and on the power play. He carries the puck and joins the rush with confidence at lower levels, but needs to even out his game at the pro level. He’s still learning the defensive side of things and still is susceptible to chasing the puck around and getting lost. He can make and take some physicality but physically he’s a work in progress as he lacks pro strength. Can take retaliatory penalties at times. Still a raw player with a good amount of upside.
Bystrom has already signed his entry-level deal with Dallas but will be loaned back to MODO where he shoot for a spot on the senior team.