Overcoming a groin injury which saw him miss the two Twenty20 internationals, Bell,who was run out, made the top score of 56 at Lords to leave England on 181-4 after 42.3 overs before the rain came down.
Play did resume with England, who had omitted Warwickshire's Jon Trott from the starting eleven, making 225 all out from 49.5 overs.
England, whose next game is at Edgbaston on Wednesday,bowled very well early on with James Anderson,Liam Plunkett and Stuart Broad collecting seven wickets between them and reducing seven batsman to totals of six or less.
As usual,Shiv Chanderpaul was the main resistence making 53 not out. Paul Collingwood put in a superb throw to see off Edwards for the final wicket with the vistors on 146 and give England a win by 79 runs.