Put into bat, England rode on a strong 113-run opening stand between Bell, who struck his eight ODI ton, and Moeen Ali (46) to give the visitors a good start only to see the script reverse in the final 10 overs.
Ali's wicket, who missed on a fifty after falling to James Faulker (1-53) in the 23rd over, was followed by James Taylor (5) as Australia seemed to pull things back a bit.
But rookie Gurinder Sandhu had other ideas as the young medium-pacer finally got Bell in the 43rd over to check England's surge.
Sandhu's well disguised slower ball got the better of a well set Bell, when the opener looped the ball to mid-off for Mitchell Starc to complete the formalities.
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A ball later, Sandhu struck again, this time sending captain Eoin Morgan out caught behind for a first-ball duck.
Wicketkeeper-batsman Jos Buttler (25) tried to add some quick runs in the end but Australia came up with an improved bowling show in the death overs to allow the visitors just 27 runs from the last five.
Looking comfortable at 244 for two at the end of 40 overs, England saw a big slide as runs were hard to come by and the wicket-fall also did not help their cause.
Australia have won both their games so far while England stand ahead of India, who are winless, in the points table with a win and a loss from two matches.