The Giants tried to downgrade the careless conduct grading of the rough conduct charge, but it was upheld.
Bedford's one-match suspension means he is the latest player this season to be banned under the league crackdown on dangerous tackles.
He was banned for his tackle on Sydney player Oliver Florent during last Saturday night's loss to the Swans.
The Giants also accepted Brent Daniels' one-game suspension for his high bump on Jake Lloyd.
"We find Bedford's conduct to be careless," the tribunal ruled.
"Bedford's recollection that he only had a light grip on Florent's left arm is not consistent with the vision. Vision captures Florent's arms pinned in the tackle and a rotation-type movement to bring Florent to ground with excessive force.
"Florent's arms were secured so he had no opportunity to use either arm to protect himself.
"We find Bedford breached the duty of care owed to Florent. Given the features of the tackle, the tackle was such that a reasonable player would not regard it as prudent in all the circumstances."
The loss to Sydney snapped the Giants' seven-game winning streak, while Port go into Sunday needing to turn around a run of four-straight losses.
Also on Tuesday, West Coast player Bailey Williams fronted the tribunal to contest his one-game rough conduct suspension for a high bump on Essendon defender Mason Redman.
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