There are as many opinions about bonsai soil as there are bonsai
However, many people have had good results with an inorganic mix made from 1/3 akadama, 1/3 pumice, 1/3 lava rock. Piece size is determined by the size of your bonsai, generally, but 3/16" - 1/4" is a good size for many medium size and larger trees. Smaller trees in smaller pots you will want to go smaller - like 1/8". I sift my soil components and have a couple of Home Depot buckets on the side where I keep smaller piece sizes (though not dust/fines - you never want those regardless of your mix).
Green Thumb I'm talking about the local nursery chain like the one in Lake Forest. They have their soil components displayed as bags hanging on their wall. Just ask them about their smallest pine bark mix. You are looking for small chunks with a minimum of dust/fines.
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For development purposes, I was pretty successful with a mix made up of mostly pumice and a little pine bark, but these trees were usually planted in large pond baskets or Anderson flats where drainage was never going to be a problem. For trees in bonsai pots, I would go with the traditional blend with no organic, and I didn't have to worry about the soil clogging until the tree's rootball had grown and taken up all the void space in the soil.
You never want "dirt" in any bonsai mix. That includes potting soil, sand, dust, organic fines, anything that turns into mud in water. Even if used in small amounts, that muck will simply fill in the void space in your soil mix and create pockets of anaerobic activity. Roots need oxygen to live, and if you choke them off they will die and rot... exacerbating poor soil conditions. This includes clay products that might start as pieces, but break down quickly when wet (think cat litter). There are a million clay products out there that may look like great soil components (as a replacement for akadama), but be very careful if you use them without experience. Even branded products can differ in their make-up from region to region. What works in one place may not work in another - because the product is different.