It's been some time since I've ridden that route, so hopefully someone with fresher data will chime in.. but AFAIK there's really only the Alexander Avenue route up from downtown Sausalito to the bridge. The route is highlighted in yellow on Google Maps. Start from Bridgeway and head south; when you get to a hill, start climbing. Alexander Ave has good, wide shoulders and lots of bicycle traffic. The vehicles are moving at speed but it's not especially challenging for novice cyclists - apart from the hill ;-) The only part I didn't like was the narrow tunnel that passes under 101 just at the northern approach to the bridge, but that's only about 20 yards of riding.

Years ago you could ride under the foot of the bridge and wind through the old military installation, but I think that route closed in 1999 or so. Anybody know if it has re-opened? Edit: gpelpel says it is open. That's the quieter route, for certain.

Watching the Blue Angels from the bridge is a great spot - I still vividly remember being able to see the pilot's helmet as he crossed over us about 150 feet off the deck.