The Reagan administration, champion of free enterprise and less government, has sidetracked a bill that would all but eliminate the Interstate Commerce Commission and remove the last vestiges of federal regulation from the trucking business.

The bill, written by the Transportation Department in April and backed by the Office of Management and Budget's regulatory review team, disappeared from view about the time it became widely reported that President Reagan was seeking a new endorsement from the Teamsters' union, which backed him for the presidency in 1980.

The Teamsters and trucking industry interests oppose further deregulation because the limited deregulation passed in 1980 has aided many of the industry's competitors and driven down freight rates, not to mention the wages of unionized drivers.

It is widely assumed by transportation lobbyists and Capitol Hill observers that a deal has been struck between the White House and the Teamsters: the legislation will languish in the White House; the Teamsters will support Reagan for reelection.

A Teamsters official said, "It looks to me like the thing has been put to rest." But he dismissed suggestions that this was because the administration is courting Teamsters political support.

"I just don't think" the administration wants "the hassle of going through more transportation deregulation," he said. "I don't see any political benefit to anybody."

Or the White House may have made a simple political judgment that this is not the time to move the legislation.

"I don't imagine we would be thinking of making any dramatic changes in this session," said Rep. James J. Howard (D-N.J.), chairman of the House Public Works and Transportation Committee, which would have to consider the bill.

But Sen. Bob Packwood (R-Ore.), chairman of the Senate Commerce, Science and Transportation Committee, which also would have to consider the bill, is planning hearings for September on the trucking industry, regardless of whether there is administration legislation to consider. He is known to strongly favor further deregulation.

It is generally assumed that if the administration bill does not move during this session of Congress, few will want to take it up in 1984 with everyone's attention on the elections.

Traffic World, a trade journal, said the deregulation bill was scheduled for Cabinet Council discussion on June 8, then pulled from the agenda after a meeting between Reagan and Teamsters President Jackie Presser, who has called trucking deregulation disastrous and claims it has cost the union 300,000 members nationwide.

No meeting between Reagan and Presser occurred in the White House, a spokesman there said. It is known, however, that White House aides have met with Presser.

Another White House official said the bill was "on hold" and confirmed that it had been dropped from the June 8 agenda. It was "pulled off," he said, because of concern that it had not been discussed with all "affected people on the outside," including Presser and "the Hill."

Top Transportation Department and Interstate Commerce Commission officials said their understanding is that the legislation is alive and that the White House has not reached a final decision.

Transportation Secretary Elizabeth Hanford Dole, in a written response to questions prepared by the Senate Commerce Committee for her confirmation hearing in January, listed "deregulating surface transportation, particularly the trucking industry," as among the most important issues she would face.

As prepared by the DOT, the bill would totally deregulate the trucking, barge and freight forwarder industries (freight forwarders arrange for the transportation of goods).

The only areas left for the ICC would be oversight of a few remaining railroad and interstate bus issues, some truck safety questions and consumer protection. Additional legislation would be needed to transfer those functions elsewhere and formally "sunset" the ICC, a longtime goal of the Republican Party's conservative wing.

But some administration officials argue that trucking deregulation is already 90 percent complete and that removal of the remaining governmental presence is not worth the political hassle.

The Motor Carrier Act of 1980 and ICC rulings have made it easy for truckers to enter and leave the business, open new markets, reach contractual agreements with shippers and change their rates on short notice. In the past, any of those actions was subject to a potentially lengthy ICC proceeding if someone objected, and the burden of proof was on the applicant.

The deregulation act reversed that; the burden of proof is now on the complainant and the result has been a dramatic decrease in challenges to trucking initiatives.

The paper-work burden for truckers--a target the Reagan administration elevated to high visibility during its early months in office--has increased since deregulation.

A trucking company is required to file a tariff, which lists its rates, each time it changes those rates. Before deregulation, tariff filings for trucks, buses and railroads numbered about 400,000 annually. This year, the ICC is expecting 1.3 million filings.

What does the ICC do with this paper work? It usually just files it. In 1982, with 907,179 tariff filings, the ICC fully suspended only 28 and partly suspended two.

The ICC has proposed several regulations that would reduce tariff filings or ease the procedure so as to provide exemption from the 30-day notice requirements that still apply to trucking tariffs. It is the opinion of the commission staff, however, that "the total elimination of tariffs will require legislation," chief of staff Robert G. Shepherd Jr. said.