Bairstow was stumped by wicketkeeper Alex Carey (32) when the England batter assumed the ball was dead and walked out of the crease, sparking a 'Spirit of Cricket' row as Australia won the test and took a 2-0 series lead.
As the visitors headed to the dressing room during a break, several MCC members were seen booing and heckling the players before stewards stepped in to defuse the situation.
All three MCC members were charged with "abusive, offensive or inappropriate behaviour or language". One member was expelled, the second got a four-and-a-half year suspension while the third was banned for 30 months.
"The actions of the three individuals in the Pavilion on the day in question fell well below the behaviour expected from our members," the MCC said in a statement.
"The penalties set out above are the consequences of breaching the Club's Code of Conduct."
England eventually won the third and fifth tests to draw the series 2-2 as holders Australia retained the Ashes.
