Career
Bjargardottir made her first Icelandic team at the 2000 Summer Olympics in Sydney. There, she failed to advance into the semifinals in any of her individual events, finishing twenty-seventh in the 200 m freestyle (2:0522), and thirty-sixth in the 100 m freestyle (5844). At the 2004 Summer Olympics in Athens, Bjargardottir shortened her program on her second Olympic appearance, swimming only in the 200 m individual medley.
Bjargardottir challenged five other swimmers in heat one, including two-time Olympians Marina Mulyayeva of Kazakhstan and Vered Borochovski of Israel.
She raced to fourth place by 0.62 of a second behind 16-year-old swimmer Park Na-Ri of South of Korea with a time of 2:22.00. Bjargardottir failed to qualify for the semifinals, as she placed twenty-seventh overall for the second time in the preliminaries.