Conal Bonnar was born in Cashel, County Tipperary, in 1969, the twelfth child in a family of thirteen which includes two siblings, Cormac and Colm, who won the All-Ireland Championship with Tipperary. His forename reflects the family ancestry. Bonnar’s parents came originally from County Donegal and Conal’s name was taken from the ancient name for the county. He was educated at Cashel CBS. His father Pearse holds the unique distinction of having played for Cashel King Cormac's in a West Tipperary Junior Football Championship match at the age of 72 years.
Bonnar played his club hurling with the local Cashel King Cormac's club. He enjoyed some success at underage levels, and in 1991 he won a senior county championship. It was the club’s first-ever senior county title. This triumph was later followed by a Munster club hurling title.
Bonnar first came to prominence with Tipperary in 1987 when he won a Munster minor title with the county. He subsequently joined the Tipperary under-21 panel and won both Munster and All-Ireland titles with his native-county in 1989. The following year he won a second consecutive Munster under-21 medal.
Bonnar was drafted into the Tipperary panel for the 1988 All-Ireland final. The event attracted plenty of attention because he became the third Bonnar on the panel and, to be drafted in at that stage of the championship, was an indication of the potential of the player. Unfortunately, victory went to Galway on the day. In 1989 Bonnar was a full member of the Tipperary team and he captured his first senior Munster medal. This was later converted into his first senior All-Ireland medal following a final victory over Antrim. His performance throughout the championship earned Bonnar his very first All-Star award.
Two years later in 1991 Bonnar captured a second provincial medal before later winning his second All-Ireland medal following a win over Kilkenny. Once again his performance in the championship earned him a second All-Star award. In 1993 he won his third Munster medal, however, Tipperary were later beaten by Galway in the All-Ireland semi-final. Bonnar won his first National Hurling League medal in 1994. Three years later in 1997 Tipperary lost to Clare in the Munster final, however, in the first year of the 'back-door system' Tipp later qualified to play Clare again in the first-ever All-Munster All-Ireland final. Unfortunately, Bonnar ended up on the losing side for a second time. In 1999 he claimed a second National League medal before retiring from inter-county hurling.