Jeppy, it very much depends on the circumstances, the child's capabilities and a lot of other factors. We pulled difficult child 3 out of mainstream because he simply wasn't coping with so many things, including the unsupervised non-classroom stuff (which includes getting to and from school). We initially transferred difficult child 3 to a more distant school. When he was still attending the local school we had him going by public transport. There was no feasible public transport to the highway school but a few parents carpooled.
If difficult child 3 had continued in mainstream to high school he would have done what his siblings did - used public transport except when it was practical for me to provide transport. However, I knew he would have been a huge target for local bullies - it was bad enough for the older three kids.
I would discuss this with your son and lay it all on the table - how much extra it costs in terms of your time and energy as well as the extra fuel costs. Under what circumstances it is better value (or better sense) for you to drive him instead of him using public transport - transporting a delicate science project is one possible reason. Or a different start time due to an extra class or a school excursion. The snob factor doesn't wash, but he could be using it as an excuse, there may be a more valid reason that he is too ashamed to tell you about - if he's being bullied, for example. He needs to be honest with you. If he is genuine about feeling that bus travel is too low class - well, praise him for being honest but explain to him that if you used that benchmark for everyone and everything in the family, there would be a lot of things you would all be doing differently and chances are it would also be costing you a lot more. The snob factor does have some validity in some circumstances - my mother always said that it was low class to eat at the table with a newspaper under your place; instead you should always use either a tablecloth with place neatly laid, or a placemat. If you ever use a newspaper, then you've really stopped caring...
We all have our standards.
In Australia, as a rule, the rich kids travel by public transport too. And the adults - difficult child 3's school principal, and deputy, travel by public transport. I know, because a couple of times I have travelled with them (and got a lift when we got to their station). I drive a lot, but mostly because I am disabled and can't walk far. Where I can, and where I know parking would be a problem, I use a combination of personal car and public transport.
Try and get your son into the mentality of "My other car is a..." and frankly, it's the air he projects that is more important than how he travels.
There's also "do to get" - if he's not using his time at school wisely, then maybe he needs to reconsider his level of commitment, especially if he's wanting you to make a greater commitment.
In other words, what are YOU getting out of any extra effort to take him to school? What can he do to make it worth your while to drive him? It would give him extra time - will he use that time to study?
If you drive him to school, then you are investing more in him and his education. That investment has to pay off or there's no point. He needs to learn that this is how the world works. Nobody owes him anything, Not at all.
Marg