You can begin training your adenium as a bonsai when it's a seedling. I have made a number of posts where I have removed tap roots, or even cut off the bottoms entirely to grow new centipede style roots. But you will probably want to wait until they are at least a couple of years old before you go moving them into a bonsai pot, if it's shallow. You need to take steps to either cut out and flatten and spread the roots over time to work towards using a bonsai dish, or you need to slowly lift your plant up and up over time to expose the roots.

If you don't care about the roots showing, or your pot is deep enough, you can move it into the bonsai dish much sooner but keep in mind that if it's a snug fit or has little media, it may slow your plant's growth down considerably. Generally bonsai pots are for display and are used after you have worked through the primary push with growing the seedling.

Pruning can be done at any size, but wiring is trickier and needs to be repositioned very frequently if the plant is young and growing fast - or just wait until it's larger and mature before you wire, when it's reached a point you can grow it harder (drier) to slow growth. Otherwise you risk scaring the branches if the wire is on too long and becomes snug. You can add ties and weights to help shape branches at any age, even young, if you are careful. Easier done when the plant hasn't been watered a while so the branches are less brittle and more rubbery.

You can definitely remove the tap root (or tap roots) and begin growing more side roots to train at 6 months and up, as I have tested this on a number of my seedlings with success. I personally would advise not doing it with tender seedling that hasn't been through it's first winter to harden off.

If you want to post photos of the plant in question that you'd like to use, as well as the pot, and your plans on how you would like to train it, we might be able to give you more specific suggestions. Most of the time though you'll want to work towards a specific goal and then move the plant into the bonsai dish at a later time when the plant is large enough to suit it. If the pot is too large now, it may retain too much moisture in your mix and be more likely to rot.

Here's a recently revived thread you might enjoy about pruning, but also potting higher to expose the roots. There are some examples of adenium in bonsai style pots further down, some of them fairly small.

https://www.gardenweb.com/discussions/1643099/2014-pruning-q-and-a-section-co-op?n=65