Bleakley left her job as the host of The One Show in June, after the broadcasting corporation withdrew its contract offer amid speculation that the Northern Irish presenter was considering offers from rival ITV.
Following her departure from the BBC, Bleakley signed up to host ITV's rebranded morning show Daybreak alongside former One Show co-host Adrian Chiles.
The Daily Mail reports that Norton told the crowd at Salford's Radio Festival that while he understood Chiles's decision to join ITV, he thought that Bleakley had made a foolish choice.
Norton said: "I can understand why Adrian Chiles did it, but Christine Bleakley - bonkers. [The One Show is a] fantastic job."
He then joked: "Do you know when they come in? Three o'clock! And they finish at 7.30pm."
Bleakley is reportedly upset that Daybreak's viewing figures have dropped to around 600,000 following its launch last month.