Bresnihan was born in Waterford in 1944 and educated at Gonzaga College, Dublin before qualifying as a doctor at University College Dublin (UCD). He was married with a son and three daughters and died in 2010.
After qualifying as a doctor, Bresnihan specialised in rheumatology at Guy's Hospital in London before working with Morris Ziff at the University of Texas Southwestern Medical School before returning to Ireland to set up a laboratory at the UCD Medical School and St. Vincent's University Hospital. During his career he wrote a number of papers, two books and contributions to works on rheumatalogy. In 1991 UCD created a chair of Rheumatology for Bresnihan and in 2009 he was honoured as a "Master" by the American College of Rheumatology.
Bresnihan made two British and Irish Lions tours. He was called up as a replacement for the 1966 British Lions tour to Australia and New Zealand but did not play in any of the internationals. He was also selected for the 1968 British Lions tour to South Africa and played in three of the internationals against South Africa.