Capped at Ireland youth and Under-18 level while playing for Cherry Orchard, Bayly made his debut for Leeds United as a substitute in an English League Cup match against Southend United on 24 October 2006. On 26 October 2006, Bayly signed a professional two-year contract with Leeds. Bayly made his full debut in the final game of the 2006–07 Championship season away to Derby County. However, it was a debut to forget as he was shown a straight red card attempting to headbutt Craig Fagan. Bayly was released by Leeds early on during the 2008–2009 season despite featuring on a few occasions for Leeds during pre season. During his time in England he also played for the Republic of Ireland U19's.
Bayly joined Sporting Fingal before the start of the 2009 League of Ireland First Division season. He made his League debut on the opening day of the 2009 season against Waterford United In an extraordinary season he scored the goal that clinched Sporting's promotion to the Premier Division against Bray Wanderers in a play-off and then six days later won his first senior medal winning the FAI Cup at Tallaght Stadium following Fingal's 2–1 victory over Sligo Rovers. Despite a successful season at Sporting Fingal, Bayly parted company with the club at the end of the season.
Bayly signed for Shamrock Rovers on 15 March2010. He made his debut as a substitute the next day at Tallaght Stadium. He scored Rovers' equaliser in the Europa League tie against Bnei Yehuda Tel Aviv F.C. in the first European game at Tallaght Stadium. In total, Bayly scored 3 goals in 35 appearances for the Hoops.
Bohemians
In February 2011, Robert signed for Pat Fenlon's Bohemians just in time for the new season. "Boccer" made his debut for the Gypsies in a Setanta Sports Cup match against Portadown on 1 March but due to suspension would have to wait til the fourth league game of the season until he could make his league debut for the club. This came in a 1–0 defeat to Galway United at Dalymount Park. He scored his first goal for the club against Shelbourne on 25 April in an EA Sports Cup tie at Tolka Park. Bayly left Bohemians in October 2011 after 26 league appearances for the club. His last appearance came against Shamrock Rovers on 5 October in a 1–1 draw.
In December 2011, Robert signed for Roddy Collins' Monaghan United team. On 18 June 2012, the club announced their withdrawal from the League of Ireland and all of their playing staff were released by the club.
Robert joined Longford Town on 26 July 2012. He made his debut for the Midlands club the very next day in a 3–1 away win over SD Galway at Eamon Deacy Park. He was released at the end of the 2012 season.
In July 2016 he signed for former boss Roddy Collins at Waterford United. He made an impressive debut against Limerick in the RSC. He scored a long range stunner as they gave the runaway league leaders a very good game but a late flurry of Limerick goals saw them run out 5-1 winners.
