When I give talks about growing orchids, and the subject of potting media comes up, what I tell the orchid people holds well for bonsai. "You can grow bonsai in just about anything, IF you understand how to water that media, and how the water you use, the media you use, the shape and size of the pot you use, and the fertilizer you use interact. If you understand all these factors interact, you can use whatever you want."
If you do not understand all this, then follow the advice of someone who is successful, has bonsai you have seen that look healthy, someone who is growing in a climate similar to your own. Evaluate their advise, try to see how the factors listed above interact. Then try out their suggestions.
Compost is a perfectly good addition to a growing media in certain situations. It is not a component for all situations, I mostly use it in the vegetable garden.