Bradley was the first player to win a major using a belly putter, at the 2011 U.S. PGA Championship, but has since been followed by fellow countryman Webb Simpson at last year's U.S. Open and South African Ernie Els at the 2012 British Open.
Golf's governing bodies, the United States Golf Association (USGA) and the Royal and Ancient (R&A), proposed a ban on anchoring putters to the body in November.
However, U.S. PGA Tour commissioner Tim Finchem has come out against the change, raising concerns about different rules emerging in different competitions.
Bradley is against the change and is also upset by the reaction of fans and some in the media.
"I take great offence to people calling me a cheater. I think that's unbelievable," he told reporters ahead of this week's Honda Classic.
"It's been pretty difficult especially lately. I'm being called a cheater more than ever by fans, by some writers.
"It's really tough. I can't imagine how people can say that to me or to anybody out here. I'm sick of it to be honest."
Finchem raised his opposition to the change on Sunday, a stance which Bradley applauded.
"I'm very proud and it makes me feel good that my tour, the tour I play on, has my back," said the U.S. Ryder Cup player.
The proposed new rule by the governing bodies, who argue putters should swing freely and not be anchored to any part of the body, would come into force in 2016.
"I realize this is going to be an issue now for the next couple of years at least," said Bradley.
"I hope the USGA thought about us players before they did this because it's been really difficult on me and I know it's been really difficult on some other players too."
Bradley said much of the abuse had come online but that he had also been heckled at tournaments.
"A lot of it is on Twitter which is ridiculous anyway, I know. I do read it and I shouldn't," he added.
"There are silly fans that will say stuff. There's the occasional article that comes out, there was one recently that came out that I couldn't believe.
"The word cheater, I mean, it's amazing that people can say that. It's probably the worst thing you could ever say to an athlete."
(Editing by Tony Jimenez)