Bonnar was born in Pittsburgh the fourth of five children to George and Mary Bernadette (Wilson) Bonnar, both of whom are deceased. His dad was a butcher and meat manager for Thorofare Markets and his mom was the consummate homemaker. 

He attended Saint Gabriel of the Sorrowful Virgin School and graduated from Seton LaSalle High School. Bishop-elect Bonnar is a graduate of Duquesne University with a B.A. in Social Communications. He received his S.T.B. from the Pontifical Gregorian University, Rome and was ordained a priest for the Diocese of Pittsburgh on July 23, 1988.

Bishop-elect Bonnar served as a parochial vicar at St. Vitus, New Castle, St. Rosalia, Greenfield and St. Thomas More, Bethel Park. He served as pastor of St. Bartholomew, Penn Hills, St Bernard, Mt Lebanon and Administrator of Our Lady of Grace, Scott Township. He is presently pastor of St. Aidan, Wexford.

He served as Rector of Saint Paul Seminary, Director of Pre-Ordination Formation, Director of Vocations and the Director of the Permanent Diaconate. For the Diocese of Pittsburgh he served as Secretary of Parish and Ministerial Leadership and the Vicar of Clergy.

For 12 years Bishop-elect Bonnar was chaplain of the Pittsburgh Steelers and is currently editor of The Priest Magazine which is a national publication for priests published by Our Sunday Visitor.

Bishop George Murry, the fifth bishop of the Roman Catholic Diocese of Youngstown, died in June following a battle with leukemia.