I second what Shibui says regarding the role of mycorrhizae.
In good conditions with plenty of fertilizer and water, mycorrhizae will not be needed for the continued health of your pines. Much of the chatter regarding mycorrhizae comes from North America where their climate is considerable colder. In these situations, mycorrhizae serve an important purpose in assisting trees access organic nutrients. See in cold temperate environments as found in North America (check their climate data - you'll see what they regard as "cold" is rather different to us), microbiological activity occurs too slowly to efficiently breakdown organic matter into nutrients available for plant growth. (Dig a bit deeper, and you'll find advocates in North America for chemical fertilizer use especially during colder months for this very reason). Think of the difference in the breakdown rates in composts heaps during summer vs winter - it's all related to the same effects of environmental temperatures on microbial activity. In these situations of cold environments, mycorrhizae acts like a catalyst and accelerates the process allowing nutrients to become more easily available. They also confer some protection against soil-borne pathogens.
Such environments don't really exist for the vast majority of Australians. Moreover, bonsai culture is an artificial construct with plenty of supplied nutrients and water. Thus not having mycorrhizae won't do any harm.

Basically what I'm saying is, if your pine looks sickly, then perhaps it might be something else other than the lack of mycorrhizae causing it grief.
However, if you do still wish to encourage mycorrhizae, certainly all of the previously stated advice regarding inoculation with the soil off another pine tree, whether it is a bonsai tree or not, will do the trick. Just remember mycorrhizae are species specific meaning that not just any type will establish in just any tree. This fact means that the mycorrhizae from Australian natives may not establish themselves on exotic species like pine because the mutualistic interactions between host tree and mycorrhizae are extremely specific. Think parasite-host relationships where the parasite only infests certain hosts - e.g. heartworm only affects dogs and very rarely humans - but in this case the mycorrhizae isn't a parasite. Oh and don't be conned into buying mycorrhizae inoculant from some business here or overseas. See mycorrhizae spores are just floating in the air constantly anyway. Best part is these spores are completely free of charge and will grow naturally where the host tree and growing conditions (i.e. climate, nutrient levels, moisture levels etc) are correct. Mycorrhizae inoculant purchased from some lab may not even grow in your climate or even on your species of tree so you're better off just saving your money.
Hope this clarifies rather than confuses.