As part of her tour, the royal watched live filming at Ealing Studios in west London.
The star said: "I think I have to sweep the red carpet and get there early and get the polishing gear out.
"I'm not due to be working that day but everyone is really excited."
Catherine, who is due to give birth next month, met Downton Abbey's on-screen stars, as well as the behind-the-scenes crew.
Fifty-one-year-old Bonneville, speaking at the Tric awards on Tuesday, said he enjoyed showing people around the film set of the drama.
"I'm pretty good at showing people, I know every inch of Cora's bedroom, if I'm allowed to say that," he said.
"It gets put up and taken down and rebuilt so often for other things; so I'm very good at spotting the joins where they haven't put it back together properly."
Scenes in the kitchen, servants' quarters and working areas of Downton Abbey, and some of the upstairs bedrooms, are filmed at Ealing Studios in London.
Highclere Castle in Hampshire is used for exterior shots and other interior filming.
Downton Abbey has won various awards and by the third series had become one of the most widely watched television drama shows in the world.
On Tuesday, it won the Tric drama programme of the year award with a ceremony held at London's Grosvenor House Hotel.
Fans of the programme are still waiting for news of whether there will be a seventh series or not.
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All the stops were pulled out on the set of Downton Abbey as the cast prepared for a visit from the Duchess of Cambridge, according to Hugh Bonneville.