I dug a couple oriental bittersweet, the non-native invasive species. There is a native species, looks very similar, not sure if I could tell them apart. They are easy to take care of. Very winter hardy - through warmer half of zone 4. For most of the country, winter protection is just setting pot on ground in shade.
I use the same potting media I use for maples & other water loving deciduous trees. Water frequently enough they never dry out completely. Full sun to half shade. Growth is ''tighter'' - shorter internodes - in full sun, but they do grow in pretty heavy shade.
Vines in general, are pretty much grown like deciduous woody trees. And unless you collect a spectacular twisty trunk, you grow them a segment at a time like you would "build a deciduous tree", by this I mean you don't worry about branches, or front or anything until you have your first couple segments of trunk as thick as you need them. Bittersweet does seem to back bud well. And I believe they sprout adventitious buds between internodes easily. For grape vines, most buds will be at the nodes, with little or no back budding in the internode area. Otherwise, I don't think there is much difference in technique between the two.
Because they are a vine, they are slow to trunk up. A 2 inch diameter bittersweet might be a vine 20 to 30 feet long. The vines I found were all very straight near the ground, all the twisty parts were too high up in the trees, to high to air layer a twisty segment off. So I dug up a couple 2 inch diameter trunks and planted about 4 inch segments in tall 4 x 4 x 6 inch pots. Thought was I might use these for exposed roots down the road. We'll see what the roots look like when I repot. When collected while dormant, there is no need to collect a lot of roots. They root easily. The one below is the only picture I found, I have half a dozen in pots floating around the yard. These were collected April 1016.
Plan is to let the running branches grow out until they are about half the diameter of the 4 inch segment of trunk that is barely visible in the picture. This may mean 10 feet or more, they are slender vines naturally. When they are that thick, I'll pick the one going in the "right'' direction to make the second segment of trunk, chop it back to a segment about 2 inches long, remove the rest of the branches, reducing it to a stick again, let it back bud and grow out. When I have maybe 8 to 10 inches of interesting trunk, I'll start keeping branches that are in good spots. It will be an endless cycle of letting branches (vines) get long, then reducing the bittersweet back to a simple trunk line, until I have a trunk with maybe a 3 or so inch diameter trunk above the nebari, and good taper to where I decide to keep branches.
I am planning on making it a cascade, Another reason for the tall pot. But it will be 5 or more years before I will have enough trunk to worry about design.
I did collect a 4 inch diameter, 6 inch tall stump of bittersweet. I was disappointed. The smaller diameter vines all put out new growth at top where I chopped them. The larger, older stump only put out shoots from around the base. This defeats the purpose of collecting the larger caliper trunk. But I will keep it one more year and see if I can get a back bud more than an inch above the soil line. If I do, the lower branches will be removed and the tree built from the higher up bud.
ROOT CUTTINGS, I can't find a photo, put I also collected some thick twisty roots, maybe one inch thick, and I potted a couple of these up. One sprouted new shoots from the top of the cut root. Eventually the exposed part of the root will develop bark and look like a trunk.
For styling also read about wisteria. The same "let it run rampant then prune back hard" is used for wisteria. Grapes, Porcelain berry, bittersweet, and any number of vines can all be grown basically by the same techniques. Each species will have some specific adjustments, but most of the techniques are quite similar.
Best is if you can find a twisty already thick enough for the bonsai you envision segment of trunk, and then either dig it up, if it is at ground level, or air layer it out of the middle of the vine. Most vines root easily, grape, bittersweet, wisteria, and many others will root easily when air layering.