Don't know as last bicycle rode it in,,, 1973, very steep and no shoulder. DANGEROUS. But then 2 friends and I bicycled all the way up and across most of CANADA, which is Much Wider than shown on a map. The best Adventure 3 25yr old "boys" could Share! Suggest you call and ask the County Sheriff. If it's closed still, try the Saratoga road to Skyline and down another road, that will be almost as hard. On day 2 we biked from WG to Saratoga to Skyline to Frisco and a Quaker friend's mansion in Sea Cliff, sleeping on the livingroom floor with a picture window view of the Golden Gate Bridge! Dream with Friends! The Best "vacation", such hard work, I Ever had.
Many bikes were going both directions on our way up and back. Fine day (a Monday). Not busy, so was safe for all.
I see bicyclists up there lots of times.
We cycled to the observatory last October, no problem.
I don't think there should be a problem with bikes.
Thanks! Your answer is awaiting moderation.