She adds that she is "a northerner and a woman and a fairly down to earth person - that might be the first time there has been that combination here. That, combined with my business expertise, (shows) we do need to expand the appeal. It's about being inclusive."
One aim in her first seven weeks has been to meet the staff - and she has already succeeded in meeting more than 550 of them, giving her the opportunity to observe their "great passion and commitment", she says.
Biggs joins after one of the toughest years in RHS history, which saw a 10 per cent cut in staff - "a less than ideal year", she acknowledges, while making it clear that further cuts are "not my focus".
In her first few weeks she has moved quickly to patch things up with the BBC, after new RHS president Elizabeth Banks said the organisation, which covers RHS shows as part of a lucrative contract, had "gone downhill" and was "dumbing down" by not using Latin plant names. "There are absolutely no issues between us," says Biggs. "The BBC is a fantastic organisation. It is a marriage made in heaven for us - the two organisations fit perfectly together."
She says the biggest surprise to her since her arrival has been the breadth of RHS activity. This is despite her 18 years as a member and visits to the RHS garden at Wisley near her home in Surrey, Chelsea and the Hampton Court shows.
"I discovered really important bits of what we do that I didn't know about and that I think we have hidden from the public because of a modesty about what we've got. The science side of things is amazing - the research that goes on."
She is quick to counter any suggestion that the RHS has spread itself too wide to the detriment of its core activity: "Arts, science, education, community and horticulture - horticulture is always at the forefront." On links with the trade, she says "we are in this together" - communicating messages about the Award of Garden Merit (AGM), for instance. She says: "I'd love us to be seen as the charity of the industry," adding that she thinks many people don't realise that the RHS is a charity.
She says the RHS can help the trade by continuing to give nurseries platforms at shows and to promote bursaries better. She is also keen on promoting AGMs more. On the commercial side, Biggs says things like the RHS's art collection are little-known. She explains that the 16th century prints look good enough to be reinvented and framed as prints for modern walls.
The RHS's education programme, meanwhile, is "amazing, not just because it teaches kids to garden", but also because it teaches them where food comes from and how to grow it.
Inevitably, the Government's flagship policy of the "Big Society" comes up in conversation. Biggs says parents and friends of a school in Battersea she visited recently came together to clear a nearby site to make it into a garden. "That link of community and the importance of horticulture and the RHS has to make the Big Society," she comments.
Britain in Bloom, she believes, can help the RHS become more "accessible and relevant to a wider base of all ages and communities", a phrase that sums up Biggs's approach.
She says the question of growing membership is "probably the biggest single objective after ensuring the team is happy and focused". But there is no longer a target after several years of plateauing at 360,000 members.
Biggs admits she is envious of the National Trust's four-million membership: "It would be easier if we had the trust's portfolio. If we had the funds maybe we would have gardens in every county so everyone could go, but we would need to win the Euro Millions lottery several times over before we could do that."
She says most charities, such as the RSPB, Born Free or Oxfam, don't have a physical entity. "If we say we can't grow because we don't have more gardens or shows, we need to demonstrate how important the work of the charity is. It's a very tough time to start trying to grow, but that also gives us a bit of time while we're in an element of recession."
Ultimately, she concludes, the RHS needs to widen its relevance and appeal beyond Chelsea and its gardens: "We can appear to be quite scary because we are so knowledgeable and if you are a novice on a housing estate we can be quite daunting." The RHS website is the vehicle that she hopes will drive the change as something appealing to children and able to inform the public more clearly on "the things we do".
1983-99 Product executive, Kuoni - youngest director, first female and first non-Swiss to be appointed to the Kuoni board.
1999-2008 Managing director, Kuoni
2008-10 Managing director of scheduled businesses, Thomas Cook
2010 to date Director-general, RHS