Sen. Paula Hawkins (R-Fla.), the major sponsor of legislation creating Radio Marti, reacted angrily this week when the U.S. news service targeted for Cuba didn't start.

The failure to begin broadcasting, Hawkins said, was "one of the worst cases of bureaucratic bungling in the four years I have been a U.S. senator." Urging that Radio Marti start on an abbreviated schedule, she said, "It only takes two people to run a radio station -- one to flip the switch and the other to talk."

Hawkins cited a Dec. 5 meeting with President Reagan and Attorney General-designate Edwin Meese in which she discussed the urgency of getting the station on the air by Jan. 28, the 132nd anniversary of the birth of Jose Marti, who is known as the father of Cuban independence. Hawkins said this week, " Reagan agreed that this was a good idea." But the United States Information Agency, which has been organizing Radio Marti, never announced last Monday as the start-up date.

Radio Marti was created by the administration to give Cuban listeners an alternative to Radio Havana. The bill authorizing the broadcasts from Marathon, Fla., was passed 18 months ago. In the meantime, the start-up has been hampered by long waits for personnel security clearances and questions raised by American broadcasters about potential jamming of their outlets. USIA spokesmen have maintained that the service is "making progress" and will commence when it has enough people for a "quality program," which could air 14 1/2 hours a day. The agency is still searching for a new director, following the departure three weeks ago of Paul Drew, who this week cited internal disorganization as the reason he left. "There was an inordinate time spent on things not for radio," he said. "It was screwy. I said to myself, 'This is ridiculous. I can't make it work.' "

Hawkins said of the controversy this week, "Castro ran our immigration policy in 1980, and now he is running our radio broadcast policy."