After an apprenticeship at
Manchester United, and at the same time as
Johnny Giles, he returned home to play for
Home Farm. In August 1959, he signed for
Cork Hibernians. Bailham joined
Shamrock Rovers in 1960 and as a striker, he was top scorer in the
League of Ireland on two occasions, 1961–62 and 1963–64. On 20 August 1962, Bailham scored his only headed goal for the
Hoops in a 5–5 draw against
Drumcondra. In February 1963, he scored four times as Rovers hammered
Bohemians 7–1 at
Glenmalure Park. In August 1963, he scored a hat trick of penalties in a 4–1 win over
Limerick. Bailham played 5 times in European competition for the Milltown club. He scored a hat-trick in his last game for the
Hoops on 27 September 1964. He scored 49 league and 12
FAI Cup goals in the
Hoops. Bailham emigrated to London shortly after, but as he was still technically a Shamrock Rovers player, he could not sign for an English league team. He joined
Cambridge City and also had spells at
Worcester and
Wimbledon. He was the Southern League Premier Division top scorer in 1965–66 with 37 goals. ==International career==