Dryburgh began his senior playing career with
Murrayfield Royals. He moved to England to play for the
Nottingham Panthers in the
British National League in October 1956. However, he returned to the Royals as he was unable to find suitable employment as an aircraft fitter in the
Midlands. The Royals remained unbeaten in the 1957–58 season. He then returned to England in 1959 to play for the
Southampton Vikings, scoring four
goals in his debut game and finishing the season as the team's leading
points scorer. After starting the 1960–61 season back with the Royals, Dryburgh finished the second half of the season with the Vikings. In 1961, Dryburgh made his only appearance for the
Great Britain national team at the
World Championship Pool B tournament in Switzerland. The team were undefeated in the tournament although they finished runners up. Dryburgh joined the
Brighton Tigers at the start of the 1961–62 season and remained with them for four seasons. With the Tigers, he scored 205 goals and 262
assists for 467 points in 131 games. After the ice rink in Brighton closed, Dryburgh played for Liège in the Belgian league and made occasional appearances for
Fife Flyers, Perth Panthers and the homeless Brighton Tigers. ==Post playing career==