Bobby Kennedy started his career at Coltness United and after trials with Queen of the South and Clyde he joined Kilmarnock in 1957.
Kennedy signed for Drogheda United in January 1973 and made his League of Ireland debut on 4 February at Lourdes Stadium.
[3] On 16 October 2021, it was announced by Manchester City, that Kennedy, along with teammate Stan Horne and the families of teammates, Harry Dowd and Paul Hince would be receiving winners medals for the Division One championship-winning season in 1967–68 during half-time at that day's Premier League match against Burnley at the City of Manchester Stadium, after the club's official request to the EFL, that medals be awarded to Stan, Paul, Bobby and posthumously to Harry, was approved in January 2021.
Kennedy and his family remained in Bradford while owning various clothing shops along with his wife, Barbara, in Manchester and the North West of England.
[4][5] His son, Graeme, played football to a semi-professional level, as a goalkeeper, before coaching at the academies of FC Halifax Town, and then Bradford City.