The 31-year-old was charged by the FA after he reacted angrily to being sent off during the Championship clash with Ipswich Town earlier this month.
Bamba confronted the referee, fourth official and manager Neil Warnock after being shown a red card, and he will now miss the Boxing Day clash with Brentford.
"The main charge was thrown out, we are delighted. He got an extra game for the extra aggression when he came off, which he deserved," Warnock told BBC Sport.
"We will miss Bamba for the Brentford game. I thought it was a good hearing. As far as I am concerned that is water under the bridge now. We have spoken, I can't see it happening again.
"I said to the commissioner, I was hoping he could show me more aggression. He's only been booked once this season, as a centre-half."
Bamba has already served his original two-match ban.