The Warwickshire batsman struck a patient 138, the 10th Test ton of his career, as England finished day three of the second Test on 440-8 – a lead of 21.
Bell shared a 143-run stand with all-rounder Tim Bresnan, who added a career-best 74 not out in only his second Test match.
Bresnan must now be looking to build on the slender advantage by leading the tail in replicating the same resistance as their hosts when play resumes on day four, before the England bowlers go in search of quick early wickets.
But even though just two days remain, Bell believes a result is still possible.
“We’re obviously going to play to [win],” Bell said. “It’s a fantastic wicket but hopefully we can get bid of a lead and come out and go in hard. Generally things speed up a bit in the final two days.
“It was nice to get a hundred. We had to bat the day out and get in a position to push on and try and win the game.
“With the heat in that second session, it was hard work. It was a part we really had to get through.”
Bangladesh, however, were left aggrieved by a number of debatable umpiring decisions which they believe went against them.
Bresnan was lucky when a close-in catch was claimed on five, while Matt Prior might have gone lbw on nine before he went onto make 62.
Tigers’ Australian coach Jamie Siddons said: “There were probably three or four decisions I was unhappy with. Hindsight makes it easy for me to be critical but that’s the game.”