He treated golf as a second career, said his daughter, Sara Lynne. The day after he retired from IBM, he got up at 6:30 and said he was "going to the office" on the links to practice his game.
At the time of his death, he was a member of Merion Golf Club, Tequesta (Fla.) Country Club, Pine Valley Golf Club, and the Royal and Ancient Golf Club of St Andrews in Scotland.
His club championships included victories at Waynesborough Country Club; Mount Kisco Country Club, N.Y; Tequesta Country Club; and Lake Shore Country Club in New York. He won the Senior Club Championship at Merion, the Pine Valley Plate, and other amateur tournaments.
Mr. Bower loved to fly, eventually earning his pilot's license in the mid-1980s. He also appreciated music, dance, and painting.
Born in Philadelphia, he graduated from Haverford High School, and Cornell University with a bachelor's degree in economics in 1954. While there, he played varsity football and golf.
Following graduation, Mr. Bower served as a first lieutenant in the Army.
In 1957, he married Marilyn Minton, and the two raised three children in Radnor and then Chappaqua, N.Y. Starting in 1997, he split his time each year between Berwyn and a second home in Florida.
In retirement, Mr. Bower doted on his grandchildren and enjoyed family holidays. His daughter described him as a gentleman and good sport with a lively sense of humor.
In addition to his wife and daughter, Mr. Bower is survived by a son, Robert Jr.; another daughter, Marianne; three grandchildren; and a brother and sister.
A memorial service will be held at 3 p.m. Saturday, May 24, at the Merion Golf Club, 450 Ardmore Ave., Ardmore. Burial is private.
Donations may be made to the Jeffrey A. Coale Memorial Scholarship Fund, Episcopal Academy, 1785 Bishop White Dr., Newtown Square, Pa. 19073. Coale, Mr. Bower's nephew, died in the attack on the World Trade Center.