My first thought was maybe this guy was new and was so nervous he didn't want any distractions, and wanted to be sure that all the "official" safety rules he was told were followed.
I would think it takes a little while before you feel comfortable enough in one of those things to "loosen up." Some of the turns they have to make are TIGHT for experienced drivers. Plus, I don't know if you've ever noticed, but there are a lot of drivers down there who are not familiar with the area making wrong turns, cutting buses off, doing dangerous things - not to mention any pedestrians not looking where they're going. There are a LOT of distractions if you've never been to WDW before. I can definately see this beling pretty stressful for a new driver.
Then again, maybe he's just nuts.
This was NOT your typical Disney Bus driver. 
I had him one morning on the way to MGM and he was not Disney friendly at all. 
He stood outside the bus ala attention, I almost saluted him....in fact I did on the way out of the bus! 
His speach was as follows: "Good morning boys and girls, ladies and gentlemen, we are on our way to MGM and there will be NO drinking, smoking, eating, and do NOT stand up while the bus is in motion. I also ask that you DO NOT, in ANY WAY, destract the driver by asking questions while the bus in in motion. Any questions can be asked when the bus comes to a complete stop. When we get to your destination, don't stand until the bus comes to a complete stop. Don't forget your personal belongings, and your children....thank you and have a nice day!" 
That guy was something else. I worked with a guy like him a couple of years ago, and it was like having him driving the bus for us.
. One of the other passengers on the bus commented about him, how he "wasn't your typical Disney Friendly Driver." 
