Bobkov was recognized as the "Best Goaltender" at the 2009 IIHF World U18 Championships, where he backstopped Team Russia to a win a Silver Medal. He represented Russia again at the 2010 and 2011 World Junior Championships, helping the team to a gold medal in 2011. During the 2011 tournament, Bobkov served as a backup to Dmitri Shikin for most of the tournament. In the gold medal game against Canada, Bobkov came in to relieve Shikin and stopped 20 shots. In addition to securing the gold medal, Bobkov was named Russia's top player in that game.