I'm not sure what would be good with that bark, maybe some potting soil from Miracle-Grow
No, no , no. You're halfway there, don't mess it up now. Potting soil is too fine and will clog up the medium that you are trying so hard to keep free draining.
In this context inorganic means essentially small rocks. The kitty litter you mentioned earlier is inorganic as are the aquatic soil and Turface I linked to above. I had a source of Haydite, which is expanded shale, but they no longer carry it. Lava rock is a good inorganic component but is difficult to find in appropriate sizes. This material is easy to find in big pieces but I have only found small sizes over the net.
Perlite is a volcanic material the resembles Styrofoam beads, you have probably seen it in potting mixes. The problem with this is that the bags you are likely to get at places like Walmart will likely contain too much material that is too fine. Expect to throw half of it out. It's not terribly expensive but you will need a screen to sift out the fines.
You can even get grit from a local creek bed if you have one close, but again, screens will be required to remove the large pieces and fines. There is a product called oil-dri sold at Napa stores, this is diatomaceous earth, used to saok up oil spills. I have never used this and the same issues of size is always important to keep in mind.
Traditionally, Akadama or Kanuma were used by the Japanese, but these must be imported and are therefore relatively expensive.
These are all examples of inorganic materials as opposed to bark or peat which are organic. Keep looking, something will turn up. Try to locate a piece of screen with openings about 1/8". This is used as mentioned above to sift out the stuff that is too small.