The BF and I were just out in SF with a friend of ours, and we rented from Blazing Saddles on a whim. I"m a newbie to riding for the most part, and I thought it would be super cool to bike across the GG Bridge.
The bikes we got really weren't all that great (we got a tandem for the BF and our non-cycling friend, and a mountain/hybrid for me). But, this was more a spur of the moment thing, so you might have better luck if you plan/call ahead.
The ride across the bridge is on a separate path (there is NO way I would have done it if I had to ride with the cars!), and there a few sharp turns (although, it could have been exaggerated by the fact that I rode on a tandem - the friend backed out a mile or so into the ride - for the first time).
Oh, and if you want to do the Alcatraz tour, make sure you book in advance. We were doing a "drive up the coast" vacation, so we didn't make reservations and they were sold out for 4 days (we were only in SF for 2).
On the plus side, we made an unplanned detour to Yosemite Natl Park and got to see the giant sequoias.

Pictures from our vacation are
here if you're interested.