My little one (now 3) has done this on and off. He's recently been doing it round tescos and the only way I can stop him is by tickling him under the chin... I know it's the wrong thing as he then does it to get a tickle but needs must sometimes..
I know it's because he finds what he is doing boring so I do try to keep him as entertained as possible.
As you are on the bus and he seems to like stories can you make a big build up prior to getting on the bus that when you are on the bus you will both read a story. As a way of pre-empting the squealing as I know once he starts squealing and you start distracting him he'll do it to get the distraction. You could end up with a 'bus story book' specially for the trip..
Kids have a way of knowing when you want them to be quiet, and are therefore tense and I think it triggers the squealing to break the silence. Obviously no squealing would be great but maybe settle for loud talking, excitment as I'm sure other passengers will find this preferable to squealing..
As for the bus driver threatening to kick you off, I am quite frankly shocked. Yes it's annoying, but he's a young child, thats what they do! I would have some strong words for him I can say!!
That said I probably would use it to my advantage and say to little one 'Look the grumpy bus driver is cross with you for squealing' in a vain hope it might give him a shy moment and stop doing it. It would also drop the hint to the bus driver!!
If the bus driver threatens it again, ask for his full name and make a complaint, for gods sake, they obviously don't have kids!