The email has been obtained by the Liverpool Daily Post and was sent last week after Cllr Bradley was cleared of bullying and bringing his office into disrepute.
In the email, he said he was “relieved to say the least” that no action would be taken against him.
“Can I thank my colleagues who stuck by me throughout the last 18+ months; it has put a tremendous strain on me and my family, and at times I was minded to throw my hand in.
“The press coverage has been vitriolic against me, and I now hope I am given the opportunity to a response.”
The newspaper says that Cllr Bradley declined to comment.