Bryans began his association with motorcycles as a sixteen-year-old apprentice fitter, initially riding a BSA Bantam on the roads. His first competitive outing came at the 1959 Tandragee 100 on a borrowed Ambassador 199 cc machine. For the 1960 season he modified his Bantam by fitting a Triumph Terrier 150 cc engine to its frame, a makeshift combination that proved sufficient to win the 1960 Irish 200 cc Championship.
In 1961, Bryans progressed to a 1958 350 cc Manx Norton provided by sponsor James Wilson, an insurance broker, and learned his craft racing alongside established Northern Irish competitors Tommy Robb, Dick Creith, and George Purvis. He made his Isle of Man TT debut in 1962, also finishing ninth in the 350 cc class and tenth in the 500 cc class at the Ulster Grand Prix that year on Wilson-sponsored machinery.
For the 1963 season Bryans arranged to ride Joe Ryan Nortons, which brought him to wider attention when he was spotted at the Ulster Grand Prix by Honda works rider Jim Redman. Bultaco signed him after he guest-rode their machines in Spain, but the Spanish manufacturer permitted Bryans to accept a subsequent offer from Honda to ride works machines in 1964. In his first season with the Japanese factory he placed second in the 50 cc class and third in the 125 cc races at the Isle of Man TT — results that confirmed his suitability for Honda's precision small-displacement machinery.
In 1965, Bryans delivered the performances that secured his place in motorsport history. Riding Honda factory machinery, he won three races and added two second-place finishes to accumulate a championship-winning total in the 50 cc class. The title made Bryans Ireland's first and, to date, only Grand Prix motorcycle world champion, a distinction he held for the remainder of his life.
Bryans continued racing with Honda through the mid-1960s as the Japanese manufacturer dominated the smaller Grand Prix classes. He retired from competition and in his later years lived in Scotland. He died at his home there on 6 August 2014, aged 72, after a short illness.
Ralph Bryans occupies a unique place in Irish motorsport history as the island of Ireland's sole Grand Prix motorcycle world champion. His career arc — from borrowed bikes on Ulster club events to a factory Honda world title in just six years — reflects both the compressed nature of talent identification in 1960s motorcycle racing and the ambition of Honda's works programme during its dominant era in Grand Prix competition.