Depends a lot on the bush obviously. Usually though there are at least "clumps" to work with.
If you have two folks we use the continuous sling
Liftex Corporation the one they call a "roundup"
We would work off the loader bucket center usually, but every situation is different.
If there was a concern, and no need for the mulch, I would just knock the dirt off, throw them in the dump truck and haul too the dump.
Around here, Dump fee's (when we do it commercially) are by the ton so volume does not matter. Some folks are set up by volume so that would change my thoughts, but here, if they were from your own home, it is already paid for. I guess what I am saying is the question would be how your local dump would charge.
Shredding, you would need to take off the roots (unless it was a rental shredder /
chipper and you did not care about the knives) For us, it would not pay out.
If it was close to our house, we dump those bushes and shrubs, let them rot down a bit, roll them around and usually bush hog them in a couple months. Just helps break down my clay and give me a bit better soil.
Hope it works out well for you however you do it. About the best thing I can say is two folks, and very positive communication between them, makes those jobs go fairly quick.