Percentage of roots is not meaningful for a tree in the ground. All the work is done by individual cells a few millimeters behind the tip of the root. These are usually far away from the trunk at the "drip line" corresponding to the edge of the canopy, The reason is simply that the ground closer to the trunk is dry and will not sustain root growth. So, if you have a leaning tree, say, roots away from the lean of the trunk will be the ones closest to the trunk. One might be able to remove one-third to one-half of the root tips of a health tree, keeping the others undisturbed to keep the tree alive, I think.
This still could be a colossal sized root ball, unless the tree is growing in a relatively small humus that filled a rock basin or is a special species like rhododendron/azalea that naturally maintains a compact root pad, so one must root prune and irrigate for at least one season to grow roots close to the trunk by cutting alternate slices around the tree with a sharp spade. Those cut ends will make new root tips as long as the ground is kept damp. Then maybe in the following spring you lift it cutting those log roots that remain and pot it up in a grow box full of a good substrate. Then you leave it until it is growing vigorously and then you begin the process of root pruning and repotting to generate a pad of fine roots right up against the trunk. Then it goes into a bonsai pot.
This is likely more than three years since it was lifted. I would guess about 5 typically, atop the 2 or 3 years of in-situ root pruning that may be necessary.
I realize it is overly simplistic, but the basic truth is that one must prune roots to make this happen. Most inorganic substrates will also induce some root branching without pruning, but it is not enough of itself, it is just far better than any organic soil in this respect. One can also use containers like colanders, pond baskets, air pots, and some loose fabric grow bags to affect air pruning of roots, saving one from the labor of taking the tree out of the grow box of substrate to do it as well as eliminating much of the temporary impairment of all the roots that comes with it.
Success totally depends upon the specie's capacity for root recovery. Spring 'as buds swell' is okay for pretty much every species, though the timing window can be quite narrow (e.g., one week) for some. After that, when new growth is extending, nearly every species has an extremely low capacity and is a very risky time to attempt lifting/repotting. Most every species, however, again has a high capacity for root recovery beginning shortly after the summer solstice that gradually ends as temperatures drop near 40F. This is a good time for almost every species of conifer and for waxy broad-leaf species.