Bycroft started his career at Notts County, though failed to make an appearance with them. He moved to Midland League club Grantham Town where he scored his first goal against Newark Town. He then moved onto Bradford City and Hull City where at neither did he make an appearance. Returning to Grantham Town, he played in their record 13–0 win over Rufford Colliery, and scored a hat-trick in the FA Cup in a 6–1 win over Ransome & Marles. He moved to Newark Town.
Syd was then signed by Doncaster Rovers in January 1936 for a fee of £250. He played for them in 501 games, both league and other appearances, including the Wartime League games. He would have been likely to have passed the club record of 417 league appearances held by Fred Emery had his career not been interrupted by the Second World War. During his time at Doncaster he was team captain. During the war he served as a police officer for the Doncaster Borough Police. Resigning in October 1946, Bycroft resumed his footballing career full-time until he retired at the end of 1951. In a game against Notts County where Syd was up against Tommy Lawton, Michael Parkinson said that: In a programme about past footballers, Parkinson also said, "He had a tackle like a bear trap."
He then qualified as a coach and working for Doncaster, he brought through players such as Alick Jeffrey. He had a brief spell as joint manager for Doncaster in February 1958 with former teammate Jack Hodgson following the surprise departure of Peter Doherty. The club was already struggling and within his tenure as manager it lost 10 of its 15 games and was relegated into the third tier. A new manager was appointed and Syd went back to coaching for a year, leaving the club at the end of that season in 1959.
Later life
Syd maintained a strong interest in the game, particularly in the Rovers. His grandson Richard Cooper was a professional with Sheffield United, Lincoln City and Exeter City during the 1980s. Bycroft died after a long illness in 2004. At his funeral, his coffin was lowered into his grave covered in a Rovers flag. A minutes silence was held before the match with Torquay United, the Doncaster players wearing black armbands during the match as a mark of respect.
