OK, if he was really sick and frantic, I would have hoped the driver would at LEAST stopped the bus and in a caring tone, have his sister help hold up something to block, whatever. And firmly coached the kids to stay seated and mind their own business or whatever.
I simply don't know what the protocol should have been and what the driving situation was, freeway, calm neighborhood, what. Try to stay calm and find out exactly what happened. I guess I would go to the school principal first to find out who to talk to. If the driver broke a rule regarding sickness on the bus, that needs to be addressed. I'm not sure there is a legal angle to take here yet.
No matter WHAT you need to support your son and daughter. I think if it were my 5 year old (I'm almost in tears reading this) I would say, "Sweetie, this is an example of something really terrible that happens sometimes. I know you feel embarrassed and that's normal. All the kids who saw you could have been in your place, and they will have bad things happen too, it's just how life is, please don't worry." and comfort comfort comfort and talk talk talk.
I might even find out who some of the kids who saw it were and talk to their parents to ask for support on how they explain it to their kids so they realize how bad your son feels and he needs to know that it's OK. Even one kid (especially an older one) approaching him and saying, "How are you man, don't feel bad, we all get sick" and putting an arm around him would mean so much. Kids won't think to do that unless their parents explain things and coach it. I'm sure lots of them went home and told their parents what happened. Maybe some of them adivsed them to offer comfort and NOT make fun of him, but you never know these days, I would follow up with some talks to them if I could. If a parent approached me about this if it happened to their child I would 100% listen and help if I could.
I would also ask that the teachers explain to the kids that this is nothing to make fun of and any one of them could have been in that situation and tell them how to act. They may only reach the nicest kids, but that's better than none. I would want this for my child and if she saw that happen to another child, she would DEFINITELY be happy to offer comfort, she would feel relieved there was a nice way to handle it.
If things don't turn hostile and legal, and he returns to the bus, maybe you could have a word with the driver and nicely ask him/her to be sure to make your son feel better. Just a, "hey buddy, how are you feeling today?" when he boards. Maybe someone from the school, can speak to the bus load of kids about illness on the bus and the right behavior.
That's all I can really think of. I'm so sorry this happened to your little guy and I hope you can rally support.