"... I do know that you are supposed to turn off the camera when you change lenses. "
I never turn off the camera to change lens and I don't know any pro that does. The first contact break turns off electric current to the lens and it is the last contact to make the circuit when installed. So there is no power going to the lens from the camera to moment you start to twist it.
As to dust getting in, I haven't noticed it but always use common sense if you are in a dusty environment. You may need more care than simply turning off the camera. A lot of the guys I used to run with don't even us lens caps or body caps. I always did and do and I suggest everyone use them. My full time photographer niece, my own niece whom I taught, doesn't' use lens caps but I have gotten her to use the camera body cap. She sells her work for a living!
Is it best to turn off the camera and put the gear in a changing bag before switching lenses? Yes it probably is. However is necessary and/ or practicle? Hey this is a case of whatever works for you.
EB
EOS 1DX and 1D Mk IV and less lenses then before!
