you mean the golden gate visitor center on the southwest side? where did you start from? what was the route?
aside, it has seemed in the past to me that the gg bridge bike policy is somewhat bicyclist centric
https://www.goldengate.org/bridge/visiting-the-bridge/bikes-pedestrians/
Pedestrians are on the East side of bridge, Bikes on the west.
We stared in SFO at the Visitors center and ended on the north side of the span well, before the Vista Point in Sausalito...