oh and by the way when we say organic what do we mean ? is it peat or compost ?
I know from another board I used to frequent that folks in the UK sometimes use the term compost when referring to their bonsai medium. In this case I believe that you actually mean compost in the sense of decomposed organic material. So if I understand correctly, no I would not use actual compost or peat in a bonsai soil. Including such material would defeat the purpose of using the free draining mix. If you include materials of differing sizes the smaller ones work into the spaces between the larger ones and impede drainage.
Some growers, especially where the climate is very dry, use some chopped long fiber Peat in their mix to help retain more water. In your situation I don't feel that would be necessary. If you do decide to include some do not use the typical, finely textured material that you normally find in many nurseries, it must be the coarse stuff chopped up a bit.
Most growers use bark of some sort for their medium usually Fir or Pine. I use Pine bark because that is what is available here. The trick is finding it in an appropriate size. Since you will only need a small amount you could easily cut chunks up with some garden pruners. Keep the pieces of a similar size as the other components. At least one size screen of 1/8 Inch (3-4 mm) is really helpful when mixing your owns soil. This allows you to exclude whatever falls through, which is too small.
BTW, you need not go the expense of using imported components such as Akadama. I use locally available materials that don't have to be imported from half way around the world. Visit this thread to learn more about bonsai soil components and and re-potting.