As Tumbleweed points out, the shuttle only runs weekends -- and only during summer months.
I would definitely not recommend trying to bike up to Muir unless you are an excellent cyclist, are used to biking narrow windy roads and upgrade to a much better bike than what most people rent.
The other down side to this plan is many bike rentals are done by the hour. So you will pay for bike to sit while you visit Muir. However, the cheapest bike rental is Dylan's I believe.
I would make this a two day venture. Do the bike to Sausalito one day. It takes about an hour without any stops. But there are plenty of stops for photos and also at the Crissy Field Center, Warming Hut or Visitor Center at the GG Bridge. All have souveniers and the first two have coffee bars with some light food offerings. I'd plan on taking at least 2 hours.
Then to see Muir either take a guided tour, HOHO, or rent a car. Tom's Tour is a good guided which is dedicated to Muir. Dylan's tour includes Muir with a city tour. City Sightseeing is the only HOHO that includes Muir.
When you say "hike a forest loop trail" do you mean you want to hike up and out of Muir? The trail within Muir is perhaps a mile into the valley and relatively flat. If you wish to do any additional hiking you will first go up a pretty steep hill to get out of the valley Muir is in. There are trail maps of the area online and at Muir. I once took the Lost Trail up to Ocean View (no more view, the trees have grown up over the decades) and then back into the Woods. We weren't trying to break any speed records but it was at least a couple of hours.
Edited: 9:48 am, January 21, 2013