Both will use one in this week's $7m WGC-HSBC Champions event in Shenzhen, but the Royal & Ancient and the United States Golf Association intend to ban their use from 2016.
Els had previously been critical of the putter, which is tucked against the stomach, but then had one in his bag when he won a second Open Championship at Royal Lytham and St Annes in July.
Less than 12 months earlier, Bradley had become the first player in the history of the game to use such a club on his way to winning a major title, the 2011 PGA Championship in Atlanta. Another American, Webb Simpson, became the second in June when he won the US Open, before Els out-putted the Australian Adam Scott to win the Open a few weeks later.
"I thought using the belly putter would be a simple decision guys could make but, the more you think about it, the more complicated it gets," said Els. "You take Tim Clark, because he was born with his arms in a way that he finds it difficult to use a conventional length putter. So I believe they [the R&A & the USGA] are going to have a couple of legal issues coming their way.
"Carl Petterson has putted using a belly putter [for] his whole career and there's Keegan Bradley who doesn't know any other way to putt, along with Webb Simpson."
Bradley added: "They're basically saying 'all those years of practice you've done are down the drain'. I hope they really think this thing through as it would be a shame for the amateur player not to be able to use a club that helps them enjoy the game better.
"They should be trying to attract people into golf rather than pushing them away."