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The sandbar at Musha Cay appears for only four hours.

One part Casino Royale to two parts Blue Lagoon, add a splash of Vilebrequin swim trunks and you have Musha Cay, the ultimate lifestyle cocktail for movie moguls and captains of industry alike. This private island gives new meaning to exclusivity; although there are enough sprawling villas, flotillas of Boston Whalers and Hobie Cats to amuse a hundred guests, a civilized cap of only 24 are catered to at a time.

Typically, one windfall-bloated blue chip books the island for $265,000 a week and invites a dozen or so people to share in the spoils. For celebrity weddings or corporate retreats, small groups may anchor yachts offshore and head in for pool time and torch-lit dinners. What manner of Svengali-cum-hotelier could pull off singular vacations at detached-home prices?

Speeding toward Musha Cay under cover of darkness, I approach a jetty bathed in moonlight. A strong hand reaches into the boat and pulls me up onto the dock. "Hi, I'm David. You've finally arrived," owner David Copperfield says. And so begins my five-day trip to the private playground of the world's most iconic and successful illusionist.

"Musha Cay is all about celebrating the big things in life," Copperfield tells me over a spread of satay and sushi laid out on the dark mahogany bar at Landings, the social hub of the island. Big things indeed. He's known to keep mum on his high-profile guests, but a quick Google search reveals that the search engine's own co-founder, Sergey Brin, hosted his wedding here (post-IPO). The location was such a closely guarded secret that guests who boarded Brin's jet were unaware of their exact destination. Bill and Melinda Gates entertain friends on the island, and when Mr. Microsoft noticed guest houses wired with iPods, he playfully replaced them with Zune music players. Flipping though the guest book, I spot Oprah Winfrey's praises alongside Jim Carrey's playful scrawl, a few pages later a beefy John Travolta in Sharpie black.

Peppered along the most pristine stretch of the Exumas in the Bahamas, Musha Cay sprawls across 283 hectares over 11 islands blessed with 40 sugar-sand beaches. Temperatures average a high of around 27 C year-round, dipping to a balmy 23 in winter. A total of 12 bedrooms are spread across five villas on the main island – each villa outfitted in styles ranging from theatrical Balinese to clean India Hicks chic, accented with artifacts from Copperfield's personal collection.

The Houdini Room at Landings displays personal letters from Charlie Chaplin, pieces of Houdini's water torture cell and a fortune-telling machine with playful, custom fortunes for each guest. A surf-side beach gym is accented with a mojo-motivating statue of Jack Johnson, the first black boxer to win a heavyweight title (a tribute that once stood at the base of the Eiffel Tower).

While the gym draws dumbbell addicts, my preferred workout here is boarding Copperfield's custom 37-foot speedboat, Midnight Express, replicated on a design favoured by Pablo Escobar, to get to nearby islands to hike the route favoured by 19th-century smugglers. The Colombian drug lord's boat was commissioned to outrun the Coast Guard; the speed this one generates is a full three decades faster, whipping my Ray-Bans off and to the back of the boat.

After my second night, I rouse fully refreshed. The king-size bed is so light, feathery and buttery soft, it's like a croissant you can sleep in.

There's a reason every detail here feels so consummately and subliminally perfect. After years of periodic residence at the world's most expensive hotels on his international tours, Copperfield knew exactly what he wanted. He curated standout items or experiences from other stays into Musha Cay, often adding his own playful twist.

As we compare notes on our top travel experiences over breakfast, he describes how he fell in love with the "mystical quality and hidden treasure feeling of the sublime Aman Resorts in Indonesia." It's easy to see Aman founder Adrian Zecha's influence on Copperfield, in the sense that every choice he has made is in service to the guest. The genius layout and effortless flow of my beach house reminds me of entire days spent ensconced in villas at Amandari in Bali. The peace and privacy Copperfield experienced there is clearly a priority here. A hospitality connoisseur, this proprietor has clearly enjoyed the luxury of not having to trifle with the usual constraints of "the bottom line." His only concern is perfection.

As a celebrity who has been nauseated first-hand by paparazzi overstepping the line, Copperfield prides himself on the zoom-lens-free zone he offers wary guests. By the second night, I start to feel the no-one-here-but-me vibe – I leave the French doors open to beach breezes overnight, my iPhone is forgotten in a hammock as I jet-ski to distant shores, I take nude outdoor showers in a Javanese grotto. For a female traveller with severe "trust issues" and skeptical of even five-star hotel security, feeling free of such perennial paranoia is the most liberating gift.

Rakishly dashing and meticulously toned – his raven coif impervious to whipping trade winds – Copperfield takes me on a speed-boat tour to survey the main island. "When astronauts were asked what they considered the most beautiful place on Earth," Copperfield muses, "they pointed to the Exumas for their vibrantly clear waters."

I agree, telling him that swimming to breakfast is like freestyling in Grey Goose.

He laughs, "Yes, it's vodka-clear isn't it? I wanted to start with the most stunning geographic canvas possible, on which to further amaze anyone who thought they'd seen it all."

Until recently, the bon vivant kept his island under wraps, guests came word-of-mouth only, and travel journalists who weren't named Robin Leach had little occasion to visit. "I wasn't ready for the world to know it existed until now," he confides, adding that with the exception of this week he never steps foot on the island when guests are present. He bought Musha Cay only four years ago, renamed the waters Copperfield Bay and set about transforming it into a parallel universe.

To justify exorbitant rates, most luxury hotels claim the ability to jump through hoops and move heaven and earth. At Musha Cay, they just get it done. You want to watch 50 First Dates on the beach with state-of-the-art sound and picture quality? You got it. That's the lingua franca of Musha Cay. Cannes' midnight projections on the beach aren't even as sharp as this. The magician tucks into a hand-woven hammock with freshly popped kettle corn while I snuggle into a chaise longue with a platter of lobster and hand-cooked chips. Drew Barrymore gets funnier when there's lobster at hand. The "drive-in" theatre experience under the stars is the most impressive option included in your stay.

As an opulent outpost catering to the world's most powerful and famous, a guest merely mentions a whimsical idea at breakfast and by sunset it's in motion. What would you expect from an entertainer whose work has garnered more than 20 Emmy wins? Copperfield spearheaded the modern American spectacle of illusion with his prime-time performances and went on to dominate the live scene with his Las Vegas megashows at the MGM Grand, grossing well over $1-billion in ticket sales during his career.

The first sign that this would be an escape from the ordinary came in the post from Island Director Cathy Daly, two weeks before my trip – she sent me a dining preferences sheet of such colour and detail it was like I'd be moving into Alain Ducasse's pantry for the week. Just before my arrival, a charter flight delivered my desired grocery ingredients to complement fresh-caught tuna, mahi-mahi, shellfish and salsas made from fruit trees grown in Copperfield's archipelago. I had listed avocado as a fave comfort food and during my stay they spontaneously brought out guacamole 'n' chips at the beach and sweet Vietnamese green smoothies at breakfast. Guests also have the run of a 500-bottle wine cellar, and a sommelier will come to arrange tastings and pairings.

It's not all sensory indulgence here on Musha Cay, though. From lusting Lotharios entertaining a bevy of lingerie models to Manhattan moguls one monocle short of being Mr. Monopoly, sporting types really get their game on at Musha Cay. Bonding rituals are a bit like a Choose Your Own Adventure book, with guests electing the genre for their getaway. A swashbuckling Pirates of the Caribbean treasure hunt? (Why not. After all, Johnny Depp's family hideaway is just "down the way" in the Exuma chain.) With 11 islands in Copperfield Bay, the hunt can be as ambitious or bogglingly far-flung as you wish.

I end my trip with a sunset champagne cocktail on a glorious five-kilometre sandbar that surfaces offshore for a mere four-hour window at certain tides. Daly has set up Bedouin umbrellas, Thai triangle cushions and a spread of fresh oysters and bespoke condiments. As our boat hits the shore and the mirage comes into focus, I turn a cartwheel in the sand as I disembark, a joyful gesture to show Daly that she has simply made my year. The sheer sophistication of the set-up is baffling. This is considered by the few who have experienced it as the true Copperfieldian coup, the moment that is – sans cliché – magic.

Mere weeks before my visit, A-listers Penelope Cruz and Javier Bardem sealed the deal, barefoot, on this very spot. The tousled siren hopped on a jet ski in her John Galliano wedding gown and met Bardem on this sand bar, strewn with white orchids, in a family-only affair.

After the Campari-red sunset, I move my belongings from the sprawling Pier House to the wee palapa roof Beach House, where the newlyweds stayed, for my final night here. I sleep in the matrimonial bed of the hottest Latin couple in Christendom.

Steven Spielberg, you can keep the Lincoln Bedroom. For a devoted fan of Almodovar's films, this is as good as travel voyeurism gets.