You don't use pine bark for its nutrient value, it's used because it retains water. The professional nurserymen like to use it because it makes watering their stock easier, and they're less likely to have stock die due to lack of watering.
In Japan, the bonsai professionals have apprentices to monitor the trees daily, if not continuously and water the trees as needed. This allows them to use a pure inorganic mix, no pine bark, no peat moss. Nutrition can be carefully controlled with fertilizer. In general, they use an inorganic soil mix, and use organic fertilizer.
The inorganic mix they use is generally based on akadama, rivers sand, and lava. Their "river sand" is different than ours. Japan is a volcanic island, and their river sand is volcanic in origin. It's rounded pellets. Akadama is rounded. Their lava rock is rounded pellets.
Anyone notice I used the word "rounded" to describe all three components?
The particle shape is important. Rounded shapes of a similar size won't compact. There will be air space in between the particles. Think of a jar of marbles. Even full of marbles, there's lots of empty space.
This shape provides for lots of exposure to oxygen, which roots need. Also provides for great drainage. But, it also means that roots and the rootball can dry out quickly. Thus the need for apprentices to be on constant alert for watering. In fact, the apprentices call themselves "watering drones"!
Akadama does retain more water than the other components, so for trees that need more water, the mix is adjusted to have a greater percentage of akadama.
Here in the USA, we substitute pumice to replace the Japanese river sand.
Now that you know about the "ideal" mix, to have to determine if it is right for you. Can you water every day? Sometimes two or three times a day? Can you set up an auto watering system? If you cannot, then maybe you have to compromise on your mix. Maybe adding more akadama is all that's needed. Some trees will do just fine in a pure akadama soil.
Or maybe you do need to include some pine bark for water retention.
The proper soil mix for you is dependent upon your ability to water your trees. Not nutrition. Nutrition is provided by fertilizer.