Born in Derby, Derbyshire, Hassell graduated from the youth ranks at Mansfield Town. Showing his versatility from the start of his career, Hassell played in both the centre of defence and at right-back. After losing the 2003-04 Division ThreePlay-Off Final to Huddersfield Town, Hassell failed to negotiate a new contract with Mansfield.
Barnsley
boss Paul Hart brought Hassell to Oakwell as part of a rebuilding process in the summer of 2004, completing his move on1 July. Despite a slow start, Hassell made 43 appearances throughout the 2004-05 campaign and gradually became a fans' favourite. He missed parts of the 2005–06 campaign through injury but played a key role when fit in helping Barnsley gain promotion from League One. Unlike two years' previously, he was on the winning side at the Millennium Stadium as Barnsley triumphed over Swansea Cityon penalties in the Play-Off Final. Hassell then enjoyed another fine campaign during 2006–07, again in the running for all the end of season awards, clocking up 42 appearances and netting two goals. In the following season, he showed his versatility to perform heroically during Barnsley's run to the semi-finals of the FA Cup. He made multiple last ditch tackles and goal-line clearances whilst playing at right-back in a 2–1 win over Liverpool at Anfield, and was outstanding in an unfamiliar central midfield position as Chelsea were beaten 1–0 at Oakwell. He was named as Barnsley's Players' Player of the Year, Fans Player of the Year and Disabled Supporters' Player of the Year for the 2008–09 season. When Mark Robins was appointed Barnsley manager following the start of the 2009-10 season, Hassell initially dropped out of the team, yet soon found his way back in due to consistent performances and a high work rate. Hassell was made Barnsley vice-captain in the summer of 2010 when Robins handed the captaincy to Jason Shackell. The 2010-11 season was another successful one for Hassell who made his 200th league start for Barnsley against Millwall in January. Keith Hill named Hassell as club captain for the 2011-12 season. Hassell had to go in goal in a League Cup tie with Rochdale on 11 August 2012 after Ben Alnwick was sent off and Barnsley had already used all 3 of their substitutions. In his final years as a Barnsley player, Hassell found games harder to come by but nevertheless always impressed when called upon. He was released by the club after ten years in May 2014. A year later in July 2015, Hassell was rewarded for his service to Barnsley with a testimonial match at Oakwell against Mansfield Town. The home side, featuring Hassell's former teammates from the 2006 promotion winning team, won the match 4–3. He is regarded as a club legend at Barnsley.
Bharat FC
In December 2014, Bobby signed for new I-League team Bharat FC. Hassell played the first ever match for the club as the I-League debutants held Dempo to a goalless draw.
Return to Barnsley
After leaving India, Hassell took up a position as Head of Recruitment for Barnsley's Academy in 2015. He now serves as Academy Manager at Oakwell. He also took up golfing with the clubs shirt sponsor Kevin Beckett and the Kevin Beckett golf society but after four years of trying he realised he was not going to be successful especially after not being able to use a driver to tee off with; he only used to use three clubs, one being a putter.
Personal life
Hassell is a committed Christian and he credits his faith as helping him overcome his temper and giving him an abundant sense of peace.