Coming from Europe, I have been living in San Francisco for a month, and this is my first visit to America. In two months, I will have to go to Los Angeles for a meeting.
Obviously, taking the plane from SFO to LAX would be the fastest solution. As this question says, taking a bus would be cheaper.
But are there other advantages of taking the bus, for someone discovering the country? For example, is there nice scenery to observe from the bus or such things?
In fact, your potential for scenic views will be higher on virtually any mode of transportation other than the bus (plane, train, private car, boat).
There is quite stunning scenery along the coast. Amtrak's Coast Starlight follows some of it, between San Luis Obispo and Oxnard, and a seat can be had for as little as $60 coach. But keep in mind that this trip will take a minimum of 12 hours from Oakland to Los Angeles, that there is only one train a day, and this train is frequently delayed.
Renting a car and driving gives you the most flexibility to enjoy coastal scenery along routes such as the 17-Mile Drive and Pacific Coast Highway. Of course, a one-way rental is costly, fuel is astronomically expensive by U.S. standards along parts this route, and as you can imagine, driving along oceanside cliffs is exhausting.
Buses do not take the coastal route for the same reasons, aside from some tour buses that may take three or four days to make the journey. The scheduled passenger services all take the straight, fast, flat route through the Central Valley along Interstate 5. As you can imagine, a freeway trip amidst heavy truck traffic passing through an endless series of farms and ranches is not particularly memorable.
The bus does offer certain advantages over flying, but I would rate them all as moderate.
Cost. An advanced purchase one-way Megabus ticket between Union Station in LA and the CalTrain terminal in SF runs around $34 (and can be as low as $10). The ride is about 7-8 hours. An advanced purchase Southwest Airlines ticket from LAX to OAK starts around $69, with a block time of around 1½ hours. Keep in mind too that on a long bus journey, you will be taking a meal at a truck stop, probably overpriced and of poor quality.
Convenience. The necessity of airport transportation and security screening makes the time savings of a flight less dramatic, especially when services like California Shuttle Bus offer stops in several neighborhoods. On the flip side, LAX, SFO, and OAK do have relatively convenient bus or rapid transit connections.
Comfort. The bus is arguably more comfortable and offers more amenities, but this is offset by its much longer travel time. For example, many buses on this city pair offer in-seat power and WiFi, whereas few of the aircraft do; however, the need for either is diminished on a 90-minute trip. By the time my bus would trudge through Kettleman City, I could already be checking email in a cafe in Santa Monica.
Reliability. LAX and SFO are prone to fog at certain times of the year that is heavy enough to cause flight delays or cancellations. On the other hand, there are so many flights between the two areas (dozens and dozens of flights if you include nearby airports) that it is easy to be re-accommodated on a later flight the same day.
In short, if you have money to spare, I'd fly. If you have both time and money, I'd take the train. The bus is a viable option, but it is a compromise.
Fairly obviously, yes, you will see more. There's the long road, the bits of the coast, the various small town you travel through or past.
Then there's the passengers. I find you'll either get 'weirdos', or you'll meet some really interesting people to talk to. People seem more keen to chat on buses than on planes, for some reason. Trains even more so (have you considered that option?), but personally if I have the time, I prefer ground transport to air transport. You see more, get more of an experience, and it's often cheaper to get from the bus station to my hostel than from the airport too.
Finally, there's the food. Don't overlook this - airplane food these days, if it exists, is often fairly basic. I've found some fun little diners and so on that the Greyhound or other buses stop at, and it's been worth it for the experience. Still haven't forgotten 'World Famous El Bambi' diner in the middle of nowhere, Utah that the Greyhound stopped at back in 2001/2002.
Depending on where your meeting is, and what else you plan to do in the Los Angeles area, consider doing neither, and renting a car instead. "Los Angeles" is not just one place, but rather a huge sprawling expanse. Once you get there, you are still likely to be far from where you want to be, with no way to get to your intended destination unless you have a car. Therefore, even if you take a bus or train, you would still want to rent a car once you get to L.A.
The difference in the price and time is pretty substantial.
Taking the bus will cost you around 40$ to 50$ according to Busbud while a flight can cost anywhere between $100 and 250$ for a one-way ticket according to Google flights.
A flight will take roughly an hour and a half (plus the time for getting to the airport, going through security and leaving the airport).
A bus ride will take roughly 8 hours.
The amtrak is another option but twelve hours is too long. Having taken an Amtrak from Montreal to New York which took 11 hours, I can attest that taking the Amtrak for a long distance route is long, slow and dreadful.
