Bullying, when I used to go to school, was a problem that teachers professed a strong desire to fight (something that I have little doubt that they genuinely had) and yet were in most cases completely powerless to prevent. Bullying was a problem that either you dealt with yourself, or that you put up with until it inevitable went away when you reached more mature levels of education. Telling off is the first stage. When this almost undoubtedly fails, detention is the next step. This tends to have more of an aggravating effect than anything unless the bully didn't really mean to cause harm in the first place. When this fails then the next step is to suspend (or "exclude" in modern UK school jargon - as if the bully is missing out on a big load of fun by not going to school!) which, for the bully who now feels alienated and completely uncaring of any of the institutions of school life, also has no effect. Beyond this, a school is all but powerless.
The school bus problem makes this lack of effective methods of punishment all the worse. This is for two reasons. Firstly the unfortunate victim has little choice but to weather the storm of whatever the bully has in store for them, since there is no escape and often no other way to get home. The second is that what limited punishment can be inflicted, is all the less easy to apply thanks to the fact that events taking place on the school bus are off school property, and then even if the teacher involved doesn't want to use this as an excuse, it makes crime difficult to pin on criminals, and makes it unclear whether or not it is the school's business to intervene.
Thus, with rare exceptions, schools tend to be impotent. This brings me to the point that either you need to deal with the problem yourself or not bother, grin, and bear it. And you don't want to just grin and bear it, that's just wrong: justice should be served.
So, dealing with the problem. The first thing to remember is that nine times out of ten a bully is really not clever. In my time I've tried all the methods in the book, both in defence of myself and others: smiling, laughing, arguing, ignoring. None of it will work, since frankly your average bully is just too much of an idiot - plus the constant alienation from the system imposed by the school punishment has almost certainly left them feeling angry and a bit lonely, so after a long day at school being forced to try and do work they don't understand and don't want to understand, they probably aren't in the best of moods.
What does this leave us with? Either you're back to the rolling over and letting them walk all over you, or you hit back. Hard.
There are two methods to do this. The objective is to break through the stupidity to whatever there is underneath; there is some humanity in there somewhere I assure you. The second thing to remember (other than that your opponent is thick if you recall) is that they really aren't likely to be as tough as they look. Some of them are, in which case your only option is to keep your distance and not hit back, which is not really a satisfactory solution but necessary to avoid getting pulverised unless you happen to be a black belt in something or other. But if they're not, you have your opening.
Let's assume then that they're not so tough, just nasty. Your first method is, I would argue, the truly vicious and unpleasant one that should only be used as a last resort. I really can't comment on the effectiveness of this method because I've never had the heart (and probably not the wit) to use it. This is to go metaphorically for the jugular and get them where it really hurts; an attack on the fact they are probably poor, have an alcoholic father, and have no hope in life will almost certainly hit them where it hurts. Personally, in the heat of the moment, I don't think I could do this without making an idiot of myself. But used effectively (namely if there is truth in your words) the power of such an assault could be verging on the atom bomb. If said bully is a wimp then potentially you will have just crushed their spirit to such a degree that effectively you've just bullied them which was not your aim. The other possibility is that you'll simply enrage them, in which case recourse to method two is likely to be necessary.
I may sound somewhat glib, but I am actually very serious. This is the only method that I have used and found to be effective against the bully, who generally will have chosen you for no reason except that you seem to be an easy target. You probably guessed it: violence. I do not seriously advocate this as a method as it is likely to get out of hand, but if you have no option then go for it, preferably when the bully is not expecting it and will not be able to hit back before you're gone. It sounds dirty and it probably is, but challenging them to a duel in the school playground will just end in disaster, so hit and leave. I don't say hit and run because running will destroy the air of strength, but hitting and walking away before the bully has realised what just happened is surprisingly effective. If you can do it such that the bully doesn't lose face in front of his friends for example then I personally would argue that you need not fear reprisals and escalation and general disaster. But clearly this could easily occur.
The conclusion then is that this is no easy problem to answer. Attacking the problem by getting the school to sort it out may be the most civilised way of dealing with the problem, but it is also the least effective. Violence on the other hand, even verbal, has a great deal of potential to go wrong. Nevertheless being cool and collected will always be an effective shield, and a well-applied (and preferably discreet) punch can solve a surprising number of bullying problems. I don't advocate it; merely I argue that it can, in the right circumstances, work.