By Car, Big Sur
If you ever needed a car, this is the place though a hearty soul could bike it as well. Mass transit is next to non-existent and even if you could find a bus, you wouldn't be able to stop when/where you wanted. We drove up from Santa Barbara and it's a good three hours and 160 miles of fairly scenic driving to get there.
It's a good hour of amazing road from there to Big Sur proper but don't rush through, this is what you came to see in the first place. Carmel is a very scenic 45 minutes north and that is generally where the Big Sur area is said to terminate but don't let that deter you from driving further north as the scenery up that way is no slouch either. Besides, if you are going to San Francisco (and why wouldn't you?), there's another 3+ hours of beautiful coast yet to see. You could knock an hour or so off by taking the inland highway but unless you're rushed for time, that would be a silly thing to do.
Like with 99% of the States, the only way to see this Highway is by car. I am sure there are bus tours, but I couldn’t imagine not stopping at will to take the pics you want.
Be careful, this could be in the warning and danger section, but the road is very curvy, much without guardrails, and is driven by a gaggle of rubberneckers. Do yourself a favor, and if there is something you see that you want to look at, pull over. There are plenty of spots for you to do so. Don’t put yourself or anyone else in danger.
Also, I recommend if you take this drive going south. My suggested tour is seeing Monterey/Carmel, take your time driving Big Sur, see Hearst Castle, then stay in Santa Barbara a couple days before driving North on Hwy 101 back to SF / NorCal. This route will allow you to skip LA. This is planned.
If you fly in and are planning on renting a car from Monterey airport, consider an off airport location. You can save $30-50 per day compared to the airport location rates!
I got a compact rate of $23.99 at Hertz on Del Monte in Seaside (4 miles away) and they came and picked us up "off airport" at the corner of the airport entrance where there is a Comfort Inn (Olmsted Dr). (They pick up but cannot advertise they do as it's Nationals catchphrase) A two minute walk from the MRY airport terminal. A compact rate was $25.99/day.
Short walk, big savings!
The drive between San Simeon and Monterey is certainly beautiful, but keep in mind that it will take longer than expected because there is an 80-mile portion which is very curvy and only a two-lane road. Average speeds in this section are less than 45 miles an hour. It took us at least an hour longer than planned to get through this stretch.
On the plus side there are quite a few turn-outs available for taking in the sights. There are also a few historic and picturesque arch bridges in the area, including the Bixby and Rocky Creek bridges just north of Big Sur. On the north side of each bridge are places to stop, look, and take pictures of the bridges. Plan on taking some time in this area as it certainly is beautiful.
A car is of course the best way the get around.
A word of caution for those not used to drive on narrow roads. As I've learned from other travellers, many people (especially Americans used to wide roads) find Highway 1 to be a dangerous road - narrow and twisty. I suppose it really depends on what you're used to. For a Slovenian like me, Highway 1 was wider than most of our major roads back home! LOL I found it easy to drive and very enjoyable. But I can imagine someone used to wide flat roads might find it difficult. So beware.
If you have a few days to spare for a vacation and coming from the San Francisco bay Area, A Visit to Big Sur is a must since this is where you will pass after going on a Jaunt in Monterey, Carmel by The Sea, pacific grove, pebble beach, 17 mile drive then to Big Sur! then off to San Simeon and Hearst Castle then Paso Robles, Santa Barbara, Solvang, Ventura and Los Angeles or go back the Bay Area via Paso Robles. The drive is about 140 miles from downtown San Francisco and 3 hours (with no rest room breaks and photo ops, ok. and no stopping at Monterey or Carmel). If you don't want to spend a lot for gas, then just take a multi-day monterey, carmel, big sur, hearst castle tour from the assorted Tour Companies in the bay Area.
No other way to get there than by car. The drive along Highway One is spectacular!!
I have seen people on bikes, but you must be in better than average shape to go the long distances up and down this road.