The district's building and operating committee will discuss limiting bicyclists to 10 mph on sidewalks and access pathways, and 5 mph around the bridge towers and in construction zones, spokeswoman Mary Currie said.
Transit officials would work with the California Highway Patrol to develop an enforcement plan, and violators would be charged $100 for speeding.
Up to 6,000 bicyclists and 10,000 pedestrians use the Golden Gate Bridge on a busy weekend day, the transit district said.
A total of 164 bicycle-involved accidents have been reported over the past 10 years, most of which were solo accidents. Speed contributed to 39 percent of the incidents.
The majority of the accidents took place on the bridge's western sidewalk, where pedestrians are not allowed. Bicyclists can use the west side on weekdays after 3:30 p.m. and on weekends.
The speed limits would be accompanied by signage directing bicyclists to stay to the inside and pedestrians to the outside of the pavement on the east side of the bridge.
If the building and operating committee approves the speed limit, it will be presented to the Golden Gate Bridge, Highway and Transportation District's board of directors on May 13.
The speed limit is being debated as officials prepare to close the sidewalks, one at a time, during a retrofit project on the bridge, Currie said.
The west sidewalk will close May 9 for four months; it will reopen Aug. 26.
The bicyclists who normally use the west side of the bridge will have to share the east sidewalk with cyclists and pedestrians. Bicyclists will have access to the sidewalk 24 hours per day, and pedestrians will be able to use it from sunrise to sunset.
The transportation district has found that about 600 bicyclists use the west sidewalk on a busy weekday, compared to 4,200 pedestrians and 1,900 bicyclists on the east sidewalk.
Cyclists must use the east sidewalk on weekdays between 6 a.m. and 3:30 p.m. and during night hours.
Up to 10,000 pedestrians use the east sidewalk and 4,600 bicyclists use the west sidewalk on weekend days. Cyclists are required to use the west sidewalk on weekend days and holidays.