Having averaged 14 in the opening two matches of the series, stunning stroke play saw Bell surpass 150 for the fifth time in Tests and third against India, as England declared on 569-7.
After Alastair Cook's confidence-boosting 95 and Gary Ballance's century on day one, England kept their foot down to take control of the contest.
Ballance added 52 to his overnight score to reach 156 and debutant Jos Buttler, the injured Matt Prior's replacement, provided late fireworks with a typically rapid-fire 85 against a set of tiring bowlers at the Ageas Bowl.
Personal records tumbled throughout the day as first Ballance moved past his previous Test best of 110, then Bell struck his 21st Test century, bringing it up with a huge six that also took him past 7,000 runs.
Not to be outdone, Buttler also got in on the act with his maiden fifty, although the wicketkeeper enjoyed a large slice of luck early in his innings.
Before he got off the mark, the 23-year-old saw Ajinkya Rahane's catch off Bhuvneshwar Kumar (3-101) given not out by the video umpire and Shikhar Dhawan shelled a regulation slip chance off Mohammed Shami (1-123) with Buttler on 23.
England declared when he was bowled by Ravindra Jadeja (2-153), with India finishing the day 25-1, Dhawan's poor tour continuing as he made just six.
The hosts resumed on 247-2 and moved along swiftly at 3.82 per over in the first session as Ballance and Bell took their partnership past 100.
Bell was the first to reach a milestone as he flicked a delivery off his pads to go past 50 for the 42nd time in his England career, and eight overs later Ballance had 150 after hooking Pankaj Singh (0-146) to the boundary.
India got a bit of luck in the following over as Rohit Sharma (1-26) found some turn and bounce to spin a ball away from Ballance, who was given out despite the ball clipping his leg rather than bat.
Having scored quickly in the opening session, the hosts were reined in after lunch, losing Joe Root (3) and Moeen Ali (12) cheaply, yet that brought Buttler to the crease and runs soon started to flow again.
After burning two lives, Buttler finally found his feet and began to punish the India bowlers with some powerful hitting.
He went past 50 in just 64 deliveries and helped push England beyond 550 before finally being dismissed, with captain Cook immediately declaring.
England's breakthrough came in the seventh over, Dhawan nicking James Anderson (1-14) to Cook at first slip.