Sri Lanka were 14 without loss in their second innings at tea on the fourth day, with Tharanga Paranavitana nine not out and Lahiru Thirimanne unbeaten on three on his Test debut.
The tourists were still 179 runs behind after England captain Andrew Strauss enterprisingly declared on 377 for eight, a lead of 193.
Bell finished on 119 not out -- the first Test hundred at the Rose Bowl -- following his unbeaten 103 in England's innings and 14-run first Test victory in Cardiff.
Together with Eoin Morgan, who made a breezy 71, he shared a sixth-wicket stand of 137 against a flagging Sri Lanka attack badly missing retired greats Muttiah Muralitharan, Chaminda Vaas and Lasith Malinga, not to mention the injured Nuwan Pradeep.
England resumed Sunday on 195 for four, a lead of 11 that owed much to a fluent 85 from Kevin Pietersen, who had come in with England struggling at 14 for two.
Bell was 39 not out overnight and James Anderson unbeaten on nought.
Anderson drove the third ball of the day, from Thisara Perera, off the back foot through the covers for four and later repeated the stroke off the same bowler -- both shots worthy of any 'proper' batsman.
Anderson struck two successive cover-driven fours off Chanaka Welegedara but, next ball, he was caught behind off the same bowler for a sparkling 27, having helped Bell put on 45 for the fifth wicket.
Bell, 78 not out at lunch, pressed onto his 14th Test century.
Late cut and square cut boundaries off successive deliveries from left-arm seamer Chanaka Welegedara took the 29-year-old to 95.
Meanwhile left-hander Morgan cover-drove Welegedara for a fifth boundary to complete an 88-ball fifty and bring up a century stand with Bell.
And Bell went to his own hundred when he hooked a Suranga Lakmal bouncer for a single to get to a century in 159 balls with 12 fours.
Morgan, who had an lbw decision overturned on review on 58, got himself out when, trying to carve Lakmal through the offside, he got an edge and gave wicketkeeper Prasanna Jayawardene his fourth catch of the innings.
England then lost a flurry of wickets chasing quick runs, with Matt Prior, who made a hundred in the drawn second Test at Lord's, out for nought.
Strauss, in a match where 155 overs have been lost to bad weather, called a halt in a bid to give his bowlers plenty of overs in which to dismiss Sri Lanka and claim a 2-0 series victory.
And they might have had an early breakthrough when left-hander Paranavitana gloved first innings hero Chris Tremlett down the legside, only for diving wicketkeeper Prior to drop the difficult one-handed catch.
