Atkins was originally on the books of Leicester City whom he joined straight from school. He was however released by City without playing a first team game and for a while dropped down into non-league football with Enderby Town. It was while playing for Enderby that Sheffield United spotted him and after an initial trial period the 20-year-old Atkins signed a permanent deal with The Blades.
The Preston years
In two and a half years at Bramall Lane Bob played 40 league games for United scoring 3 goals but midway through the 1984–85 season he was offered along with Gary Brazil the chance to goon loan to Preston North End with the possibility of making the move permanent. At the end of a season that saw Preston relegated Atkins along with Brazil signed permanently for the club for a combined fee of £25,000. With Preston now in the Fourth Division, Bob was beginning to find his feet. However, although originally a midfielder Atkins who stood at 6'2 started finding himself due to injuries playing more frequently as a centre back. It was here that Bob really started to shine. Given the nickname "Skillful Bob" by the fans due to his ability to bring the ball out of defence and look for a passing option rather than "hoof" it as many lower league defenders did he was a mainstay and a rare sign of hope in what turned out to be Preston's worst ever campaign with the club finishing 91st in the Football league. The following 1986-87 season was thought to be a turning point in both Bob's and Preston's fortunes. With John McGrath now in the Deepdale hot seatNorth End stormed to promotion with Bob's three-pronged defensive partnership with Sam Allardyce and Alex Jones, nicknamed "the solicitors" an absolute rock at the back. Atkins scored one of the goals of the season to equalise from distance away at Crewe on Boxing Day 1986. The following three seasons for Atkins were much the same with him missing only a handful of games and turning out some sterling performances, indeed he was named the club's official player of the year in 1987-88 and was also awarded the club captaincy in 1988–89.
Injuries
The 1989–90 season though proved to be his last for the club. Despite the club starting the season poorly, Bob was again a consistent performer in defence. However, an injury against Tranmere Rovers on Boxing Day 1989 more or less wiped out his season, and although he returned for the final third of the season Bob was never to kick a ball for Preston again. The following season Bob spent on the treatment table trying to overcome his injury problems, but at the end of the season he was forced to admit defeat and hang up his boots. He now lives back in Leicester.