Cook, who had buried India with three tons while totalling 562 runs in the four-Test series won by his team last year, and Bell compiled a partnership of 152 for the first wicket, breaking a 30-year record for England against the hosts in the process.
Left-handed Cook made 75 in 84 balls with 11 fours and a six while his right-handed partner was slightly more aggressive in making 85 off 95 balls with nine fours and one six.
The duo left in close succession just past the half way stage of the innings but their good work was continued by Kevin Pietersen and Eoin Morgan.
Pietersen (44 in 45 balls) and Morgan (41 in 38 balls) put on a breezy third-wicket stand of 76 runs in 9.5 overs before both fell in 12 balls to Ashok Dinda.
However, Samit Patel smashed 44 not out in 16 balls, with six fours and a six, and added 70 runs in the last six overs with Craig Kieswetter who remained unbeaten on 24 off 20 balls with a four and two sixes.
Most of the Indian frontline bowlers were expensive. Ashok Dinda, who was preferred over Shami Ahmed despite the latter's impressive debut against Pakistan in Delhi last Sunday, was the most successful with 2 for 53.
Ravindra Jadeja (0 for 46 in 10 overs) and Suresh Raina (1 for 18 in 5 overs) bowled economically on a batsman-friendly wicket.
Ashwin was expensive with poor figures of none for 61 in nine overs. Senior placer Ishant Sharma conceded 86 runs in his 10 overs, including 20 in his last, which is his worst display in his 51 ODIs while rookie Bhuvneshwar Kumar was also punished by the England batsmen.