Need a ride to Miami or Los Angeles, or New York City? For a fee, Travel Mate/The National Carpool Association will give you the names and phone numbers of drivers going your way on a share-the-cost basis.

If you're the driver, the privately owned assocition, will help you match up with potential passengers.

In this day of $1-a-gallon gas, association president Joe Bentivegna of Portland, Ore., believes in cutting the cost with additional riders. If two are making the cross-country trip, gas 50 cents a gallon each; if there are four, it's down to 25 cents. In addition, says Bentivegna of his service, "It's safer than hitchhiking."

Though it's not part of the name, the association also lists the trip plans of private-plane pilots and passengers interested in small-plane flights.

"Senior citizens and women are our best customers," says Bentivegna, who maintains his firm has never had a reported crime in its six-year history, during which, he says, they have arranged more than half a million referrals.

One elderly Seattle woman wanted to "see my country one more time," he says, and at the same time deliver her car to her son in Florida. A young couple drove her, she paid the expenses, and they "had a nice time." When a Navy man in San Francisco was ordered to Japan, he had his son transported, via the association, back home to grandparents in North Carolina.

The big advantage of such arrangements, of course, is the cost. Recently, Bentivegna says, he drove the company van with four passengers from Portland to Los Angeles at a cost of $27 each. "that's awfully cheap to go 1,000 miles."

Gary Starr, 24, of Herndon, Va., phoned the association a few days ago. He plans to drive his pickup truck to Los Angeles the first week of November. In the past such a trip has cost him $150, but he hopes to cut that cost this time by taking along at least one rider.

Not every driver, of course, is satisfied with the first potential rider who calls, or vice versa. One woman driver called to say she had arranged to take a man from her Venice, Calif., home to New York but changed her mind because, she said, "he was a dirty hippie."

"We got her somebody else the next day," says Bentivegna, who points out his firm does not screen drivers and riders.

"You choose your own partner," he says. "We're just a facilitator." If possible, driver and rider might meet before the trip to see if they are compatible.

Bentivegna, 37, came up with the idea of a cross-country carpooling association in 1973 when he was tending bar in Las Vegas during the first gasoline crisis. He said he had heard stories from the Depression about similar arrangements.

He tried it out first in Los Angeles, got some experience setting up rides for the elderly during a local bus strike, and then began to expand to several cities around the country. Four years ago, the firm acquired a toll-free "800" phone line (800-547-0933) and a small office computer that allowed it to go nationwide out of one office. Now six operators take calls daily from 10 a.m. to 10 p.m. Eastern Standard Time.

Bentivegna sees his association as one way to conserve energy. He also sees it as a way to help small-town motels, restaurants, service stations and others in the travel industry who, he says, lost money during last summer's gas shortage because people didn't drive.

The firm has undergone a couple of name changes. It started out as Hitchhikers for America and later became People's Transit. Neither projected quite the image Bentivegna was beginning to aim at.

"We got more street people in the old days," says Bentivegna, but about three years ago when the firm began accepting credit-card payments, "we started getting good people."

Bentivegna believes his firm's safety record can be attributed in part to the fact that he has credit-card information on his-clients.

Here's how he system works. If you want a ride, to Florida for example, you phone the 800 number and give the operator your name, phone number, address and where you want to travel. The fee is $25 for a roundtrip, or six months; $40 for a year; $125 for a lifetime. You can charge on most major credit cards. The association will give you the phone mumbers of anyone headed in your direction.

The system works the same for a driver looking for riders, and at the same cost. It's up to both of you to make the specific arrangements.

If you can't make contact with someone locally, the computer can widen the search, giving you, say, the number of someone in Boston headed through Washington to Miami.

The system for pilots is much the same, except the cost is $75, because, says Bentivegna, "Pilots fly more often than people drive and use the phones more."

Small-plane owner Mike Montefusco of Alexandria recently signed up with the association. He likes to use the plane he shares with a partner for vacation trips to Palm Beach, the Bahamas or Nantucket. But, as he points out to potential passengers, at least four have to fly, or the small-plane flight will cost more than going by commercial airliner.

The Aircraft Owners and Pilots Association neither encourages nor discourages such arrangements, says vice president Charles Spence. "But we believe anyone who flies in a private aircraft should know that passenger (or pilot). If you unhappy, you can't get out and walk at the first stop light." Spence suggests plane-pooling among friends.

Bentivegna now is looking at the possibility of a network of low-cost "bed and breakfast." accommodations for the traveler, based on the European example where people with a spare room or two take in overnight guests. And when Los Angeles hosts the Olympics in 1984, he wouldn't mind seeing Europeans making New York-to-West Coast driving arrangements through his association.