In the statement, issued to Sky Sports News, Bridge said: "I have thought long and hard about my position in the England football team in the light of the reporting of the events over the last few weeks.
"It has always been an honour to play for England. However, after careful thought I believe my position in the squad is now untenable and potentially divisive.
"Sadly therefore, I feel, for the sake of the team, and in order to avoid what will be inevitable distractions, I have decided not to put myself forward for selection.
"I have today informed the management of this decision. I wish the team all the very best in South Africa.