HE PIVOTED LEFT, faked the pass, then eased a one-hand jumper through the hoop. Jigme Singye Wangchuck had just chalked up another two-pointer for his team. Of course, he has been scoring points for his country ever since becoming fourth Druk Gyalpo of Bhutan.

We were enjoying an unusual bonus for tourists: watching the 25-year-old King of Bhutan play basketball.

Only days before, after flying from Calcutta, we found ourselves staring with unabashed curiosity at another figure, a tall Mongolian-looking man dressed in a robe with plaid knee socks who had met us at the airport at Bagdogra, in the Terai (subtropics) of India. We didn't want to seem impolite, but none of our tour group had ever seen a Bhutanese before.

Nim Gyalchen, 25, representing the government of Bhutan, welcomed us in his soft-spoken English aboard the tour bus. He was to be our escort and one of our guides during our visit to the landlocked Himalayan country wedged between India and Tibet. There is only one entry point into Bhutan, at Phuntsholing, its industrial center and link with the outside world. Phuntsholing is a three-hour drive from Bagdogra.

As we drove toward Phuntsholing along the sweltering Indian asphalt, dodging cows, chickens, bicycles, trucks -- you name it -- the situation struck me as slightly ludicrous: 10 Americans driving through India on a Japanese-made bus going to Bhutan.

Worn out by the heat, some of us dozed off, perhaps conjuring up visions of mysterious unexplored frontiers. But when our bus rolled under the huge, pagoda-like temple gate at the border, a rush of excitement woke us from our reveries, for our dreams had become a reality. We were in the Kingdom of Bhutan, Land of the Dragon.

Everywhere we looked there was a royal greeting. Royal Customs, Royal Bank of Bhutan, Royal Post Office, Royal Insurance Company . . . painted in a glowing red and gold. Phuntsholing is populated mostly by Indians, but the Kharbandi Hotel, a 15-minute drive from the border gate, was more Bhutanese. Ten or so smiling hotel employes each dressed in a kho (robe) stood outside to greet us, displaying white teeth, red-brown faces and jet-black hair. They are Asians, yes, but they do not look like Japanese, Chinese, Thai, Filipino or Korean.

The Kharbandi is really a way-station for the incoming tourists who spend the remainder of the travel day and evening in Phuntsholing, then proceed into the hinterland to the valley of Thimphu the next morning. Bound for Thimphu, our beige Toyota bus wound it way up and up, through scenic mountain passes, past gushing rivers and never-ending waterfalls. We passed rice and potato terraces neatly etched into green hillsides and watched women toting chldren papoose-style or men carrying sacks of flour, sometimes even a hog, on their backs.

In 1958, it took the late Jawaharlal Nehru seven days by horse to traverse this same route; now it takes six hours by auto. The 112-mile highway was completed in 1962 and was financed by India when Nehru was prime minister.

"I would say that Thimphu is the most remote capital city anywhere in the world," said United Nations Deputy Resident Bernard Hauser, who with his wife and two daughters, became Bhutan's first live-in American family. I met Hausner when I was wandering around Thimphu by myself without the rest of the group.

Being a tourist in Bhutan can be a bittersweet experience; exciting, frustrating, maybe a bit dull at times. Bhutan is unlike any other country I've ever visited -- beautiful, natural, majestic scenery, unusual architecture, interesting-looking people wearing traditional dress. But you're not really free to hop a bus and go to the end of the line, and accommodations are prearranged by the government.

Tour itineraries are structured and carefully planned by the Bhutan National Tourism and Travel Agency. Because facilities, accommodations and roads are limited, travel is also limited and restricted to only the western half of the country, which is less populated than the eastern half. Sightseeing is permitted only in Phuntsholing, Paro, Punakha, Wandiphodrang and Thimphu. In Thimphu, however, tourists can wander alone into the stall shops along the one main street.

All meals are eaten in the hotel because there are no restaurants. There is no "night life," except for a movie house in Thimphu that exhibits many American-made films. Tourists are kept together in groups and are escorted by a guide. Sightseeing takes in monasteries, temples, dzongs (fortress-like buildings which are governmental and religious centers), temples and the National Museum of Bhutan in Paro. A tour of a school or hospital can be arranged.

Bhutan was officially opened up to visitors in September 1974, and about 300 Americans arrived that year. Many had learned about the isolated country when foreign dignitaries attended the formal coronation that June of the young king, who ascended the throne at his father's death in 1972. Last year 1,700 tourists arrived, 50 percent from the United States. Bhutan can handle only 200 visitors at a time.

"You are not just a tourist in Bhutan. You are also our guest. But we don't want guests coming in masses like the tourists do in Nepal," said tourist promotion director Sangey, 28. He has no other name. He's not even addressed as "mister" by his staff. His rhetoric is authoritative, philosophical, sometimes glib, but his English has been perfected by the visits that he makes annually to States, Europe and England.

"We are a special country with an interesting history, situated in a remote part of the world," Sangey said. "Our past is still our present. Our lifestyle is traditional, simple. Our country doesn't do things quickly, but rather cautiously, gradually, so that we can correct our mistakes as we move slowly along. It is important to us, too, that we do not become influenced by the tourist dollar or that it becomes an instrument to tempt us to sell ourselves. We forbid any kind of tipping," he explained.

The original inhabitants of Bhutan emigrated from Mongolia and Tibet in 450 A.D. Now, about 1.2 million people live in a country the size of Vermont and New Hampshire. Through the centuries they have become a mixture of Nepalese, Tibetan, Mongolian and Indian. The Bhutanese are called "drukpas" and they speak their own language, "dzongkha," which is closely related to Tibetan. English, however, is the official correspondence of the government and nearly all street signs are written in English. Only a small percentage of the working population speaks it.

The Kingdom of Bhutan is an agrarian society in which every family raises enough food for its own consumption. A rich man is one who has a surplus. Though the country does export some timber, fruits, canned juices and agricultural products (to India), the main source of income comes from tourism.

A typical day in Timphu included, viewing dances, shopping at the handicrafts emporium (Bhutanese currency is equal to the Indian rupee which is also acceptable), visiting the Tashichhodzong, touring a monastery and walking around the town. On another day, we drove to Punakha, which used to be the country's capital until 1955. The dzong there, situated at the confluence of two rivers, was built in 1637 by Bhutan's first theocratic ruler, Shabdung Ngawang Namgyel. Punakha is in a fertile valley, rich with fruit trees and surrounded by mountains that echo the prayers of chanting monks.

In his book, "Bhutan, the Land of the Peaceful Dragon," (Vikas Publishing House, New Delhi, 1974), G. N. Mehra, who was commissioned by the late king, writes: ". . . Though obscurity surrounds the early history of Bhutan, it is closely linked to religion and is mainly chronicled by the advent and spread of Buddhism in the area. Religious incursions from Tibet into Bhutan had already started in the 7th century A.D. King Strongsten Gampo of Tibet proclaimed Buddhism as the state religion and had built many monasteries in adjoining areas [now Bhutan], one of which is the Kyichu Lhanghang in Paro, one of the first temples . . ."

The state religion is Buddhism, and the Je Kenpo, or chief abbot, rules the monastic order.

The Taktsang Monastery (meaning "tiger's nest") is one of the most sacred temples in Bhutan, visited by pilgrims from all parts of the country. Reached in two hours by foot (pony for the tourist), the site commands a sweeping panorama of Paro Valley, And on a clear day, Mt. Chomo Lhari (23,997 feet) looms in the north, straddling the Tibetan border, which is an 18-hour walk away.

The Hotel Olathang in Paro is a cluster of cottages each suited for two persons and decorated with colorful bedspreads and drapes of Bhutanese design. It is situated on a knoll overlooking part of the valley. Meals are eaten in a main dining hall with a lounge in the same building. Cuisine is simple with little variety: rice or potatoes, vegetables with pork, chicken, sometimes beef. Water is boiled and filtered. Soft drinks, fruit juices and alcoholic beverages are served. The Motithang Hotel, in Thimphu, is located more on the outskirts of the town, offering comparable meals; it is one structure with double occupancy rooms.

There are special eight-day packages offered through the government's tourist office: $977/person during high season (March-June, September- December) and $845 during off-season months. Price includes visa fee, all meals, lodging, ground transport, sightseeing and guide. (Both Pan American and Air India service New Delhi for New York, San Francisco and Los Angeles; then a flight to Bagdogra via Calcutta.) For more information and reservations contact: Bhutan Travel Service, 133 East 55 St., N.Y. 10022; (202)838-6382.

In the past, only visitors who were part of a tour group (such as Lindblad) were permitted entry. But just this year the government has modified its restrictions. Now a person does not have to be a tour member and can apply for a visa individually (allow four to six weeks). Cost is $130 a day in high season and $90 a day off season, minimum stay seven days. But all tourists are still escorted and cannot enter Bhutan or travel inside without a guide. There is no direct commercial air service into Bhutan, but Bhutan and India are negotiating a proposed air route that would link Calcutta with Paro, which is 1 1/2 hours from Thimphu. An airfield already exists at Paro, but a Bhutan International Airlines Company has not yet been set up.

In conjuction with cultural sightseeing, a Bhutan itinerary can also take in several days of trekking or a yak safari. Altitudes may reach 15,000-foot levels.

More emphasis is being put on trekking packages, from seven to 12 days and longer, because Bhutan is beautiful, uncrowded and unpolluted. Bhutan started trekking tours in 1976 with advice from Mountain Travel Inc., a U.S. tour company which has pioneered adventure trips to off-beat destinations around the world. Mountain Travel offers two trips to Bhutan during October and April. (For more information and catalog: Mountain Travel, Inc., 1398 Solano Ave, Albany, Calif. 94706; (415) 527-8100).

Diana Niskern, 38, went trekking in Bhutan with a Mountain Travel group.

"I was interested to see the flowers and birdlife and chose the spring for that reason. I've gone trekking in Nepal during the fall and winter and thought that this would be different, especially trekking in Bhutan," said Niskern, a librarian at the Library of Congress.

The country is striving to become self-reliant but is still tied economically to India which also gives "guidance" in foreign affairs under a 1949 treaty. The government consists of the king, his council of ministers and advisory council, and the national assembly.

And the king does more than play basketball. He is slowly opening up his country while seeking to avoid becoming involved in a power struggle between China and India.