Beatrice is auctioning the controversial Philip Treacy creation to raise money for charities UNICEF and Children In Crisis, the latter of which is supported by her mother the Duchess of York.
Bannatyne, who is a UNICEF ambassador, wrote on Twitter: "Right I might not love #thehat but I think it's fantastic that Princess Beatrice is auctioning it for @UNICEF_UK.
"#thehat doesn't work for me. But it's for a great cause. I've bid £5k here http://bit.ly/royalhat Can you guys do any better?"
The Dragons' Den star has already been outbid by £300 for the headpiece, which has been widely lambasted since Prince William and Kate tied the knot on April 29. A Facebook page titled 'Princess Beatrice's ridiculous royal wedding hat' now has over 134,000 fans.
"I am an ambassador for Children in Crisis and have learnt a huge amount about their work for children, and when my hat started getting so much publicity I really wanted to put it to the best possible use and try and raise some money for the children they help," Beatrice told Grazia.
"Children In Crisis and UNICEF are both doing amazing work for the most vulnerable children in the world so they were the natural choice for me.
"I really hope this idea can raise lots of money to give children a better future."
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> Read our full royal wedding coverage