He spent his entire career with Íþróttafélag Stúdenta where he won the Icelandic Basketball Cup in 1978.
In 1967 he started attending the University of Iceland and at the same time joined Íþróttafélag Stúdenta (ÍS).
[4] On 30 March 1978, he scored 11 points in ÍS 87-83 victory against Valur in the Icelandic Basketball Cup finals.
[6] In 1988, he played two Icelandic Basketball Cup games with the ÍS-b team against Úrvalsdeild club KR.
[7][8] In 1974, at the age of 27, Bjarni was selected for the Icelandic national team for the first time.