Sophie set herself the challenge to raise money for The Duke of Edinburgh's Award, which is marking its sixtieth anniversary this year.
Speaking exclusively to HELLO!'s royal correspondent Emily Nash, the superfit royal admitted: "There are certain members of the family who think I'm completely crazy.
Sophie Wessex is raising money for The Duke of Edinburgh's Award
"I think my father-in-law definitely thinks I'm mad, as does the Queen – but I know they understand why I'm doing it.
"Other members of the royal family have also been very supportive and then there are the family athletes like Zara and Mike [Tindall] who really get it."
The Queen's husband Prince Philip set up the Award sixty years ago. He was present at Holyroodhouse on Monday morning to wave his daughter-in-law off, as was Sophie's husband Prince Edward.
Her husband Prince Edward waved her off on Monday morning
Sophie and Edward's children Lady Louise, 12, and eight-year-old James were at school.
"They are furious with me that they're not allowed to see me off," said Sophie. "But it is a school day. They're coming to see me arriving at Buckingham Palace."
"I think to begin with they thought, 'Oh, Mummy's going for a bike ride, how nice.' They didn't realise quite how much commitment it was going to require and, in fairness, neither did I.
"I think my father-in-law definitely thinks I'm mad, as does the Queen," said Sophie
"They have both been pretty good with it but there have been moments where they've said, 'Oh, you're not going for a bike ride, Mummy? How long is this one going to be?'"
Sophie and her teammates are due to arrive in London on Sunday.
For the full exclusive interview pick up this week's issue of HELLO! magazine out now.