This is the conundrum I came up against--I know that you're not supposed to bare root conifers because of the micorrhizal relationship, but if you're not supposed to bare root it, and not supposed to leave nursery soil in there, what do you do?
You don't do it all at once
I killed a lot of conifers early on until I got smart about repotting. It is important to note, there is an art to knowing each tree is different, and what you can do with it before you stress it or kill it. Some trees can handle certain work, while the same species of tree in a different condition will be killed by the same work. So take everything I am going to say with a grain of salt.
First, make sure you time your work appropriately. With conifers your best window for this work is in the spring, after the last hard freeze but at least two months before summer heat. You want to have the tree awake, but give it plenty of time to recover before the heat of summer. The second window is in the fall, after the heat of summer, but with plenty of time before a hard freeze... or perhaps you can provide some minor protection via a cold frame or unheated greenhouse.
Second, make sure you understand the difference between fine feeder roots and large structural roots. The tree takes in water and nutrients via fine feeder roots. If you remove all of them, you will greatly stress the tree and might kill it.
Third, understand the big difference between a conifer that is established in good bonsai soil, versus a conifer in a nursery pot. In inorganic bonsai soil there is a lot of void space and room for oxygen exchange throughout the soil. The established conifer will have a fine mesh of feeder roots throughout the mix, so that repotting is a relatively straight-forward process of gently removing the old soil, trimming the roots, and replacing with new soil. You will often see repotting videos showing exacting this action of repotting a tree that is already in bonsai soil. However do the same thing with a tree in a nursery pot, and you very well could kill the tree.
In a nursery pot, the soil mix is largely organic and may have almost no void space. In order to breathe, the roots seek the outside of the root ball, so you have all your fine feeder roots on the outside or the bottom snuggled up against the black plastic pot. The interior of the root ball consists primarily of large structural roots - some of which can be quite long and circle in and around and through the root ball. Untangling this mess can be a major exercise in frustration, but it has to be done. Some people advocate "take a saw and cut off the bottom half of the rootball" but you have to make sure that you know what you are cutting. If the rootball consists of a large tap root that goes straight to the bottom, and then the fine feeder roots curl up the sides of the pot, if you cut straight through the rootball at the halfway point, you may sever the wrong roots. Another possibility, which has worked well for me with trees with fine roots, is to view the tree from above and think of the rootball as a pie. You want to try to remove all the soil from two opposite 1/6 slices of the pie - so that you are bare-rooting and working 1/3 of the roots of the tree while leaving 2/3 alone. Do this three years in a row, cleaning out two new slices each year, and after three years you will have barerooted your tree and replaced all the soil... just gradually.
Just going to add to Walter's comments about fertilization. Be very careful about using chemical fertilizers. It is very easy to over-fertilize, or to allow fertilizer salts to build up over time in a pot and burn the roots - particularly if you don't water heavily, and don't have an inorganic soil mix. You should never fertilize immediately after repotting, because you will stress the new roots. It is much more difficult to burn your tree with organic fertilizers, because they tend to be less strong, and often take time to break down into the soil.
. During development normally personally fertilize all trees weekly during growing/2 times weekly for conifers later summer/fall. 20-20-20 chemical fertilizer
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