I would have to agree with the posts stating this is an accident waiting to happen. Your calm dosile cattle potentially could blow up as soon as you get a rope around their neck. Then if they run off perpindicular to your ATV, over the ATV goes. Also, if the calf gets slack in the rope and starts running around your motor scooter, then you end up getting tripped up and hurt.
We had a lot of cats around our place when I was young. All of them nice and dosile, would come up and lay on your lap as you pet them. But one time I got the bright idea to practice my roping skills on a few, so I tied a honda in each end of a clothes line coard. Wound up and caught one. It started jumping, hissing, running all over. So I took the other end and caught another one(don't really know why I thought that was a good idea). Believe it or not, but it did the same exact thing. So now I have two cats on each end of my rope, bouncing, jumping, hissing... I am now wondering how I get the cats off the rope when I hear my Dad yell "WHAT ARE YOU DOING!!!!" My response was to let go of the rope, which set the cats somewhat free. One decides to run away and jumps a wood fence. Now we have a cat on both sides of the fence, seesawing back and forth. Luckily everyone escaped without too many injuries. But it goes to prove a lap cat on the end of a rope is no longer a lap cat.
Here is what I would suggest, find some local boys that are part of a roping club or do team roping or tie down roping. Any of them would probably enjoy the free practice and the chance to work their horses on fresh cattle. The younger they are, the more eager they will be to do it for free, but watch out and make sure they have a head on their shoulders and aren't going to run your cattle through a fence or put undo stress on them. Once they catch them, you roll up on your ATV, throw the calf, doctor it, and go onto the next one.