A Florida airline took the first steps yesterday that could pave the way for lower air fares to the Bahamas.

In a petition filed with the Civil Aeronautics Board, Air Florida said it would extend popular low fares it now offers travelers within the state of Florida to travelers to the Bahamas as well, if it is granted new CAB authority.

Air Florida now operates jet service between eight Florida cities using a two-tier pricing system featuring one fare for flights on weekdays and another - cheaper - for evenings and weekend flights. All the fares, even the weekday "business" fares are less expensive than those charged by Air Florida's CAB-regulated competitors.

For example, Air Florida charges $33 to weekday passengers between Miami and Tampa, and $20 evenings and weekends, compared with $38 charged by the CAB carriers. (Like intrastate airlines in California and Texas, Air Florida is regulated by a state commission and not the CAB).

"Air Florida is capable and ready to begin DC-9 service between Florida and the Bahamas, offering innovative low fares, as soon as it is given the authority," the carrier told the board yesterday.

In its petition, Air Florida asked the board to split off from an overall U.S.-Bahamas service investigation the service needs of Florida-Bahamas, or alternatively to give the entire proceeding expedited treatment.

The carrier noted that scheduled airline service between Florida and the vacation islands has deteriorated steadily over the past several years in part because Pan American World Airways pulled out of the market and because Mackey International was found by a board investigation to be having difficulties.

The number of scheduled flights on the route fell almost 40 percent since 1972, with some Florida cities losing service to the Bahamas altogether. Service from the Northeastern United States to the Bahamas was reduced sharply as well.

"The Bahamas to us is just another local service opportunity," Eli Timoner, president and chief operating officer of Air Florida, said yesterday in an interview. "Times and distances between here and the Bahamas are just like flying within the state; except for the Gulfstream and a little water, it really is a community of interest."

Because Air Florida can now offer baggage and ticketing connections with CAB-regulated airlines, Timoner said their proposal would enable travelers from the North to add round-trip, Supersaver discount he is proposing.

Timoner created Air Florida in a hurry five-and-a-half years ago when the Florida legislature passed a bill placing intrastate airlines under the regulation by the state Public Service Commission. Under that measure, airlines already flying by October 1972 would not have to get approval of their existing routes from the state.

Two airlines are due to be given approval for low-fare service to and from Chicago's Midway Airport and six Midwestern cities.