The first half was brought to life in the 20th minute by Bell's fantastic effort. A hopeful ball into the corner from Aron Gunnarsson was sliced clear by Rovers keeper Neil Sullivan, straight to Bell, who took a touch before unleashing a 40-yard-effort into the top right-hand corner of the unguarded net.
The Sky Blues almost added a second spectacular goal to their collection on 28 minutes when Stephen Wright's 25-yard-volley smashed against Sullivan's left-hand post.
Doncaster threatened to equalise when John Spicer was played through by Richie Wellens on 34 minutes but Keiren Westwood did well to block the shot.
Wellens again caused problems when he danced through the Sky Blues' midfield before forcing a good save from Westwood with his low drive.
Doncaster started the second half brightly when Paul Heffernan adjusted quickly to flick Gareth Roberts' cross at goal on 49 minutes - but Westwood made a comfortable stop.
Dean Shiels escaped Scott Dann before finding himself one-on-one with Westwood, who did well to close him down at the near post and block the shot.
City responded to the early pressure with an effort of their own in the 64th minute as Guillaume Beuzelin's whipped cross from the left was sent over the bar by the head of Dann.
Substitute Robbie Simpson could have wrapped up the win on 86 minutes but he failed to connect with Bell's cross as he slid in at the far post.
But it was of little consequence as the Sky Blues saw out three minutes of stoppage time to end a run of four straight defeats and move above their opponents in the Championship table.