As if running an airline weren't enough, 28-year-old Annabel Hoyt has had to take on the City of Bakersfield, Calif., and its civic pride.

Hoyt is the general manager of Air Pacific, a fast-growing California commuter airline that is seeking to replace United Airlines on a route between Bakersfield and Los Angeles.

United wants out, and Air Pacific wants in: It sounds perfect. Officials of the Civil Aeronautics Board would be delighted if they could find replacement airlines as easily every time a carrier used the provisions of the Airline Deregulation Act to drop a route it no longer wanted to serve.

There's just one problem: Like other small and medium-sized cities faced with the loss of the jet service they have come to know and love, Bakersfield doesn't want to let go of United, and it has been fighting hard to keep it -- through the media, at the CAB and in the courts.

Bakersfield has complained to a U.S. appeals court that it had been "virtually removed" from the air transportation system by United's elimination of its Bakersfield-San Francisco route and that the CAB had failed to fulfill its statutory obligations in assuring communities "essential" air service during the transition to a deregulated environment.

"Bakersfield is presently caught in a transitional period on the way to its future . . .," it told the CAB in a document seeking reinstatement of lost service and the preservance of what remains.

United, which has served Bakersfield for 40 years, contends it no longer can operate its jet service profitably on short trips like its Bakersfield hops. The airline has told the board it will lose about $15 per passenger -- $10,000 a day and $3.8 million a year -- if it is required to keep its three-times-daily service to Los Angeles.

That is loss the American taxpayers may have to pick up for a year under a provision of the deregulation act if the CAB cannot work out a transition plan that proves satisfactory to all parties.

The betting is on a transitional plan that allows United to pull back some of its service -- perhaps to one round trip a day -- while other airlines, including Air Pacific, Aspen Airways and Swift Aire Lines, try to show the community that they can offer reliable efficient air service that Bakersfield travelers might like -- if they'd only try it.

Both United and Air Pacific officials say that unless United can reduce its schedule the Air Pacifics of this world won't have a chance with the Bakersfield passenger.

Although Bakersfield officials railed against Air Pacific's replacement service on the San Francisco route, the airline's officials insist -- and CAB reports confirm -- that the airlines's problems stemmed from start-up difficulties and have been resolved. "Our on-time record now is better than the large airlines," Hoyt says.

Air Pacific was created in July 1978 when Hoyt and three others from Colorado bought Eureka Aero, a small Northern California airline using 9-passenger planes.

Hoyt, who has been flying since she was 16, met her co-owners through the helicopter business -- she flew helicopters in Toronto. She looked around for "an aviation opportunity" in California on behalf of them all when she was at Stanford University working on a master's of business administration degree. Eureka Aero was the opportunity she picked.

The airline has grown considerably since they took it over, renamed it and replaced the small planes with 19-seaters. Traffic has grown from 3,000 annually to 15,000 this year. Now Air Pacific has added two new de Havilland Dash 7 aircraft, very quiet, 50-passenger planes capable of very short takeoffs and landings. One already is in use on the Bakersfield-San Francisco route and the other will be used -- starting next week -- on the Bakersfield-Los Angeles route. "It's a $5 million airplane, and we have to carry a lot of passengers to make it Bakersfield-Los Angeles route," Hoyt says.