Penny Young packed her bicycle to tour the land of sultans and scents

Gold, frankincense and myrrh - the gifts brought by the three kings who followed the star. Clearly the wise men had been holidaying in Oman before arriving by camel in Bethlehem.

Gold, frankincense and myrrh - the gifts brought by the three kings who followed the star. Clearly the wise men had been holidaying in Oman before arriving by camel in Bethlehem.

A sensible choice. Not only does the Sultanate of Oman, in the south-east corner of Arabia, have a wonderful climate during our winter; it also has mountains, deserts, medieval cities, a thousand miles of seaside, as well as enough frankincense on sale (and smoking in little clay ovens in the bazaars) to last until the Second Coming.

Resisting the seasonal temptation to travel by camel, I took my bicycle to Oman. "What's that?" asked the man behind the ticket desk at Muscat airport, as I queued to check in to fly to Salalah, Oman's southernmost port, at the bottom of the Arabian peninsula. "It's a bicycle," I said. "It came from London on the plane. It's part of the trip."

His reaction didn't surprise me. I'd already got the idea, while cycling around Oman's spotlessly modern capital, Muscat, with its toy forts and well-watered lawns, that the Omanis aren't at all used to seeing foreign visitors, let alone foreigners on bicycles - although they're much too polite and dignified to make a fuss. Turbaned heads may turn, sunglasses may be lifted for a moment, but that's about it.

The bicycle was waiting for me in Salalah's arrival lounge. I loaded it up and rode out of the airport down the straight, new road lined with palm trees - the sprinklers spitting cool water. The air was hot and moist.

Haffa House Hotel was waiting five minutes away, its vast marble corridors wide enough to cycle down - which I did.

Oman is an immense country of only two million people. Towns and villages are scattered over a wide area, fringing the desert. Somehow, even in the heat of Arabia, there's room to breathe. The capital, Muscat, spreads over 50 square miles. Salalah, too, spreads itself along the Indian Ocean and is backed by a well-watered, green hinterland of market gardens and orchards of fruit.

My bicycle came in handy. I sped through the bazaars, draped with glittering cloth from India, and perfumed with the scent of frankincense - heaped on the stalls like chunks of crystallised amber. I slowed up through the green plantations to sniff the sweet, rich smell of the coconut palms, papaya, and banana trees, and emerged beside the sea with its sandy beaches, smooth as snowfields, just in time to catch the sunset. I was at the foot of Arabia. To the west lay Yemen and Hadhramaut, to the north were the sand dunes of the Empty Quarter and Saudi Arabia.

Heading out early the next morning, my destination was Taqah and the nearby rock ruins of Khor Ruri, an ancient city reputedly belonging to the Queen of Sheba. What with her kingdoms in Yemen and Ethiopia, and a fling in Jerusalem with Solomon, she got around, did Sheba. "You're not going to cycle?" the receptionist said, incredulous. "It's a long way - 45 minutes in a car."

No problem. Oman's roads are so new and well-surfaced that I whizzed along (hat on, limbs covered against the sun) at top speed, spotting baby camels grazing among the acacia trees. Oman is a country to stir the imagination. The Sumerians knew it as the land of copper, and its frankincense and dates have long been world-famous. The hand-built wooden dhows that put to sea each night and return each dawn stacked with fish are a reminder of its sea-going tradition, and that Sinbad, the legendary mariner of the Arabian Nights, came from Oman.

Oman's modern era began in 1970 when Sultan Qaboos exiled his father and began Oman's "renaissance." The country has shot from its closed existence as a medieval fiefdom to become a 21st-century state under his rule. Qaboos has a reputation as a generous (albeit absolute) monarch, who gives homes to his people, boats to his fishermen, exiles his opponents (but then invites them back), and decorates his beautiful countryside with waterfalls and models of goats. He is also said to have exquisite taste in palace interiors. It must all be a far cry from Bury St Edmunds in Suffolk, where Qaboos lived with a governess as a teenager, and where he worked as a clerk for 18 months before going to Sandhurst.

I got lost at Taqah and found myself off piste, bumping around high up on the cliffs over a black rock plateau. I was rescued by Owad Said who was cutting up an octopus when I found him. "Khor Ruri is over there," he said waving into the distance. "But there's an inlet in the way." He loaded the bicycle and me into his car and drove back to the road. Owad works in telecommunications in Salalah and goes shark-fishing on Sundays.

I flew back to Muscat that evening. They unloaded the bicycle on to the luggage conveyor belt, where it surely would have been damaged, but two Omanis - whom I've written into my will - pulled it off in the nick of time. Such are the perils of eccentric travel. I spent three days cycling 200 miles through the wadis and into the mountains around Nazwa. There are wonderful places to visit, restored castles and deserted oasis settlements that haven't changed since biblical times.

There are markets devoted mainly to the sale of goats and rifles, there are old souks and villages like eagles' eyries surrounded by soft palm trees.

The magnificent 10th-century fortress of Bahlah is surrounded by a mud-brick wall eight miles long. Nearby, the fortress home of a former Sultan at Jibreen retains the original painted cedar ceilings and a false stair built to confuse unwanted intruders foolhardy enough to try to get to the Sultan's quarters. The Sultan's favoured guests included his horse, given its own safe staircase to the bedroom.

Cycling in Oman is not for the faint-hearted. I spent a lot of time leaping off my bicycle on to the verge to avoid the crazy drivers overtaking each other as they drove towards me. There is no road rage in gentle Oman, just a lot of drivers who think their powerful BMWs and Japanese four-wheel drives are racing camels on wheels. I had a few hopeful kerb-crawlers as well, They would drive slowly past and stop a few hundred yards further up the road to wait. A female cyclist alone in a conservative Arab country is, of course, an unusual sight. But the Omanis are very civilised - they don't roar or pant like other nationalities. I merely heard a polite "Eh, excuse me" as I toiled past.

Oman has only recently opened its borders to holiday-makers, and the current policy is to try to avoid the havoc that can be wrought by mass tourism. I hope Oman is not tempted to open the Pandora's Box of sex, drugs, rock and roll, booze on the beach, and let's all photograph the sea turtles together. It's a far more civilised experience as it is, and if I were one of the three kings, I'd head back there.