Caune was born Baiba Ābere on 12 August 1945, in Stāmeriena parish, Latvia.

Soon she became a winner of numerous area school competitions, and received 4th Place at the Latvian SSR Spartakiad of Students.

In 1961 Caune began her early training as a cyclist at Tukums Sports School, under the direction of coach Uldis Mauriņš, and later she was trained by Ilmārs Janovs at Riga Central Cycling Club (CRK).

Caune worked as cycling coach at Salaspils Sports School from 1980 to 1997.

During this time she trained ten professional women cyclists and three of them won the title of USSR Youth Championship (Ilona Krišāne, Elita Ivbulete and her daughter Dace Caune).