Bonsai mix must drain well and supply constant level of moisture. Not too wet, not too dry.
Soil mixes vary from grower to grower. Some people use a totally inorganic mix such as APL (Acadama, Pumice & Lava) and control the supply of nutrients with fertilizer similar to hydroponic growing. This type of soil needs to be watered 2-3 times a day without fail. I use a three part mix: One part organic material, one part drainage material, and one part moisture retention such as baked clay. This mix retains more moisture so it only needs to be watered once a day. Bonsai soil is sifted to remove fine particles that interfere with drainage.
Placing different sizes of soil in layers as is recommended in some old books is now regarded as unnecessary. It creates a perched water table that interferes with capillary action and soil drainage.
Types of organic soil components:
Peat moss - Not recommended, acidifies soil, particles too small, breaks down too quickly.
Ground bark/landscape mix - Best alternative, higher percent of useful sizes. Found at all nursery supply stores.
Compost - If you make your own it's great but make sure it has reached sufficient temperature to kill diseases and weed seeds.
Types of baked clay material:
Expanded shale/Hadite - What concrete blocks are made from. Great material. Doesn't break down in soil. Found at gravel companies.
Baked clay - Surface-Baked clay used for putting greens in golf and on running paths in baseball diamonds. Sometimes hard to find.
Oil/Dry - I no longer recommend this product. It is no longer fired at a high enough temperature and breaks down quickly into fine clay.
Water retentive stone:
Kanuma - Soft pumice, traditional Japanese material. Very expensive.
Agricultural pumice - Perlite that hasn't been fired yet. Heavier weight than perlite, not so prone to floating or blowing away.
Lava sand - Sharp edges promote root branching. Contains iron that acidifies soil. Good material.
Blasting sand/natural aquarium gravel - Already size sorted, so no sifting needed, very heavy, particles rounded so doesn't provide as much drainage as lava sand.
Decomposed granite - Basically the same material as blasting sand, but contains a large variety of sizes. Much more waste.
Starter chicken grit - Crushed granite. Hard to find now.
Perlite - Pumice that has been quickly fired to pop it similar to how popcorn pops. White color is unattractive to some. Light weight. I use it more for plants under development. Easily found at plant nurseries.
Root systems should be rejuvenated by periodically bare rooting a wedge of soil in the pot. Keep track of where you took the wedge out on a diagram in your potting notes, because you will have forgotten where it was when the next time to re-pot comes around. Next re-potting, bare root a wedge of soil from the side opposite where it was done before. After several re-pottings, the entire root ball will have been replaced with new soil and fresh roots.