To answer your questions, the buses aren’t terrible with a scooter. Sometimes you do have to wait for a 2nd bus because there are wheelchairs/scooters in front of you.
I now use a motorized wheelchair, but I did use scooters for many years. I started with rentals and as my MS/RA progressed, I bought one for use in airports, etc. On the scooter, we hung a backpack on the back of the chair. I’ve never had anyone at Disney mess our stuff. You’ll see strollers/scooters parked with backpacks, etc hanging off them without locks.
I will say, getting on and off the bus, please turn the scooter to turtle mode and then don’t depress the level fully. You can do just fine by barely pressing it. It will give you much more control. We are at Disney now, and I have seen two incidents that could have easily resulted in vacation ending accidents because riders failed to control their speed on and off the bus. If you are struggling, just ask the bus driver to help you. However, you’ll be fin as long as you go slow.
Another issue with scooters, when you’re in the park, peopled will step in front of you and sometimes stop. You will need to be watching the entire time. When I used a scooter, I kept it very close to turtle mode all of the time and then never fully depressed the lever in crowds. I easily kept up with my family. Same with my wheelchair. I do frequently get cut off and lag a little behind, but I catch up quickly.
Please don’t be discouraged from renting one, it will make your trip much more enjoyable. If you think of any questions, please feel free to ask on here, or DM me. I have years of experience with them and will be happy to help you in any way that I can.