U.S. mass transit systems, under attack from the Reagan administration for their heavy dependence on federal aid, have made important first steps in finding other ways to generate operating and capital funds. The new financing sources range from a state lottery in Arizona to commercial bond issues in New York and San Francisco.

Transit is moving slowly away from federal dollars even though its friends in Congress have blocked, for the present at least, much of the White House's effort to cut federal transit spending, notably the proposed phase-out of the $1.1-billion-a-year operating aid program.

Creative financing for the country's 800 bus and rail systems emerged as a unifying concern this week as 2,800 transit managers and equipment manufacturers gathered in Boston for the annual meeting of the American Public Transit Association.

The conference, marking APTA's 100th anniversary, comes as the $13-billion-a-year transit industry is reeling under the blows of recession and rising costs. Ridership continues a drop that began in 1981, falling off another 4.9 percent in the first six months of 1982.

But overall, this year's delegates appeared somewhat more hopeful than last year's conventioneers. No system has been forced to shut down, and with the help of state and local governments and private financiers, major transit systems around the country are showing that alternatives can be found.

Turn-out was high at talks by officials of New York City's Metropolitan Transportation Authority (MTA), which has embarked on an $8-billion, 5-year program to rebuild deteriorating track and stations and to replace aging railcars.

Of special interest was New York's plan to finance much of the spending with private bonds, turning back the clock to the days when mass transit was private enterprise.

The bonds will be backed by fare revenues and non-federal aid. New York hopes that increased ridership will cover much of the debt service payments. It seems likely, however, that the bonds will force higher subsidies from the state and city.

But, thanks to local government backing -- both guaranteed and assumed -- MTA will acquire an enormous pot of money, without the administrative and "Buy America" restrictions of federal dollars.

Earlier this month, MTA went to the market with its first bonds, placing $250 million worth at an average rate of 9.7 percent. The issue is seed money for the purchase of 1,375 railcars that will eventually cost close to $2 billion. New York plans to put not a single federal dollar into the deal, an unheard-of proposition in an era when federal grants normally cover 80 percent of major capital costs.

MTA has raised the ire of labor unions and the Reagan administration by placing all of its car orders with foreign-affiliated companies, notably an order for 825 cars from Bombardier of Canada. But MTA chairman Richard Ravitch argues that MTA's first obligation is to its riders, and it will go where the price is best.

"The cars are going to be built in Canada, come hell or high water," Ravitch said.

On the West Coast, San Francisco's Bay Area Rapid Transit (BART) system recently sold $65 million in bonds to help buy 150 new cars. BART's bonds are backed by fare revenues and the proceeds of a sales tax dedicated to transit.

Houston, meanwhile, two weeks ago made another unprecedented decision in transit capital financing by electing to proceed with an 18-mile heavy rail system with or without federal funds.

The city's hopes for grants have run up against a Reagan administration policy barring money for "new starts" on rail. But Houston maintains it can go it alone if necessary, by using fare revenues and receipts from a 1 percent sales tax and relying heavily on supplier financing. "We would like to have federal funds, but we simply can't wait around for them," said Alan F. Kiepper, executive director of Houston's transit system.

More local governments, meanwhile, are establishing dedicated transit taxes. In July, Los Angeles County enacted a 0.5 percent sales tax that is projected to raise about $290 million per year. The new money has allowed fares to be lowered from 85 cents to 50 cents. Transit officials there report ridership has grown by about 18 percent as a result.

In Arizona, proceeds from a newly created state lottery have been set aside for transportation. Birmingham, Ala., meanwhile, plans to use a tax on beer to raise $2 million per year for transit, starting next year. Altogether, according to an Urban Mass Transportation Administration study, dedicated taxes for transit have been set up in 24 systems since January 1981.

Boston's financially troubled Massachusetts Bay Transportation Authority managed to decrease fares from 75 to 60 cents, which MBTA said resulted in 5 percent increase in ridership. The move was made possible by a state commitment to pick up the estimated $6 million loss in revenues.