The Australian children's singing group joined the internet bidding war with an offer of £17,500 ($26,760), but that was soon beaten by others keen to get their hands on the headpiece that the princess wore to Prince William's wedding on 29 April.
Blue Wiggle Anthony Field said: "We wear some pretty crazy costumes onstage, but this hat beats them all -- it could bring about an Australian republic all by itself!
"When we heard about the auction we knew we had to bid -- we're ambassadors for UNICEF and we think it's great that Princess Beatrice has chosen to support children in great need."
The 22-year-old princess has decided to sell off the curious item for charity, with UNICEF and Children in Crisis to benefit from the funds raised.
Field joked that if the Wiggles did end up with the hat they could donate it to the Australian cricket captain to use in the next Ashes series against England.
"We might give it to Michael Clarke to wear when he bats against the Poms next time -- it would certainly distract the bowler," he said.
Facebook pages have sprung up in its honour, attracting thousands of followers.
The leading bid on the eBay auction -- which ends on May 22 -- stood at £18,200 ($27,830) on Tuesday night.