Rhodesian whites, Asians and persons of mixed race began the process of handing over power to the country's black majority today by voting for four contested seats among the 28 set aside for them in the new Parliament.

At the same time, the Rhodesian Air Force again bombed nationalist guerrillas camps on the outskirts of the Zambian capital of Lusaka, this time apparently hitting the military headquarters of Joshua Nkomo's Zimbabwe African People's Union (ZAPU).

In another war-related development, the South African government announced that it would provide Rhodesia with transportation to help foreign observers and reporters get around the guerrilla-ridden country during the black elections scheduled to begin April 17.

There was intense speculation that the assistance, reportedly involving at least one C130 transport plane and a Puma helicopter and possibly more, might mark a larger South African commitment in support of the new black-led government here after the elections.

There are unlikely to be many foreign observers to the Rhodesian elections. A move to send an American team of observers was stopped in the House of Representatives Monday, and the British government has decided not to send an official delegation, although the opposition Conservative Party has said it will send observers.

Residents showed relatively little interest in Tuesday's voting as the white Rhodesian Front won three of four contested seats by a large margin. If it takes the fourth seat, as is widely expected, the party is assured control over all the 28. The Front, led by Prime Minister Ian Smith, has been ruling this breakaway British colony for the past 15 years.

Much to the chagrin of Rhodesia's blacks, Smith is certain to continue playing an important role in the new black-led government as he is filling one of the 16 other elected seats the Front won Tuesday without any contest at all.

The remaining eight places for the country's minorities in the new 100-seat Parliament are also certain to be filled by Front candidates when a special electoral college meets on May 7 to fill them.

There are 103,000 registered white, Asian and mixed-race voters in Rhodesia, but only about 23,000 were eligible to vote in the four contested constituencies. Two of them are in Salisbury and one in Umtali and Bulawayo.

The only nonwhite candidate in Tuesday's election was a mixed-race businesswoman, Esther Rawson, running as an independent in one of the Salisbury constituencies. She was given only an outside chance of upsetting Rhodesian Front candidate Dennis Divaris.

Prime Minister Smith vehemently attacked all four independent candidates last week, saying he had always regarded an independent "in the same way I look at a dog that goes on to the rugby field in the middle of a game-he just gets in the way."

The Front has held an iron grip on white politics ever since it came to power in 1964, a year before the country declared its independence from Britain. It promises to continue dominating the bloc set aside for the white, Asian and mixed-race minorities in the new Parliament and is assured by virtue of its 28 seats of either five or six Cabinet posts.

Meanwhile Rhodesian security forces kept up their pressure on black nationalist guerrillas opposing the elections by bombing two and possibly three camps around Lusaka early this morning. A government communique said all planes had returned safely from the raid but gave few other details.

Later, Smith told reporters as he toured polling booths here in Salisbury that "Russians have actually moved into positions of control in ZAPU's headquarters in Zambia and that high-ranking Soviet officers were supervising the headquarters' reorganization.

However, neither he nor the Rhodesian government provided any evidence to back up this assertion. So far as is generally known in Lusaka, the Soviets are providing substantial military assistance to the People's Union guerrillas but are not in direct control of their operations.

Reports from Lusaka confirmed that the ZAPU headquarters six miles west of the city had been hit and said that one officer had been killed and several dozen other guerrillas injured.

The announcement that South Africa was sending transport to help Rhodesia during elections coincided with reports circulating here that Pretoria is now prepared to step up its military assistance if the elections here next week are judged fair and successful.

Some unconfirmed reports say the groundwork for additional aid to help the new black-led government resists the guerrillas has been laid prior to the elections.