The logic is simple. The Observatory sits on the Greenwich Meridian at zero degrees. This means it will be the official starting point for the year 2000. "Greenwich Mean Time was set up because of confusion about time in the 1870s - every astronomer had their own meridian," Mr Bullions explains. "Its importance is internationally acknowledged."
Purists might argue that the new century does not start until the dawn of 2001. But Mr Bullions is unperturbed. "We see it as the switch from 1999 to 2000, but I don't really care - either way, it gives us a whole year."
It is just as well that he also has the next four. For the National Maritime Museum is planning a raft of licensing, merchandising and promotional activities linked to a Greenwich Meridian 2000 marque, designed by Sampson Tyrell. Local, national and international companies will be approached to participate.
There will be a 1,000 Days Countdown, starting on 6 April, 1997, when businesses will be offered the chance to buy a day in the run-up to the end of the century. For a starting price of pounds 5,000 they will be able to use the Old Royal Observatory for corporate hospitality and stage marketing campaigns or themed promotions around their chosen date. Participating companies will also have their name added to an official Greenwich Meridian 2000 Countdown Register.
Mr Bullions and marketing consultancy BDS Sponsorship are already discussing opportunities with a number of companies. "Obvious areas to pursue are watch manufacturers and jewellery companies, drinks, film, clothing, transport and travel businesses," says Richard Busby, managing director of BDS.
But, Mr Bullions concedes, the strategy is about more than the millennium.
"The National Maritime Museum faces significant fund-raising requirements for its development programme," he says. "Our ambition is to raise the profile of Greenwich and all it represents, and to create an endowment for the future development of the museum."
The National Maritime Museum comprises three sites: the Old Royal Observatory, The National Maritime Museum Galleries and The Queen's House. Government subsidy currently provides 80 per cent of its funding but the figure is being reduced. Mr Bullions' brief is to find alternative, private finance. And he must raise additional money to match applications for National Lottery funding.
Planned refurbishment, which will extend the museum's display areas by 30 per cent, is part of a capital project expected to cost around pounds 20m.
So Mr Bullions and BDS have developed a multi-tiered strategy. First, the museum will stage its own millennium exhibition featuring icons gathered from around the world.
This will dovetail neatly with the separate Millennium Exhibition to be staged in Greenwich and supported by six other "satellite" locations, as confirmed last week by the Millennium Commission.
Secondly, the National Maritime Museum will sell TV rights to broadcast live from the official Meridian to mark the start of the new century. Then there is the Greenwich Meridian 2000 marketing strategy, which will also include merchandising and licensing of the marque to millennium- related events. A range of branded merchandise will be produced.
Although everything will be geared towards the millennium, the creation of the Meridian marque is also designed to last well into the new century when the "2000" will eventually be dropped.
Mr Bullions believes the approach stays loyal to the National Maritime Museum's roots. "We're about art, heritage, museums, history: we're not Disney World," he says.
Mr Busby puts it in a broader context: "It's an integrated, overall marketing campaign that represents great marketing opportunity for the museum and significant marketing and tourist opportunities for Britain."
Making Greenwich Meridian 2000 an internationally recognised marque will be key to the strategy's eventual success, he adds. "This is where it will happen; the challenge will be convincing everyone."
However, Mr Busby remains confident they can win support in all the important markets whose calendars simultaneously mark the new millennium. "Everyone knows Greenwich is the centre of time and that this is the place the millennium will actually occur. The issue is not the legitimacy of our claim, but remembering it."