You can just boil the bark. This will get rid of any bugs that are in it. I find that sulphur spray kills fungus gnats as well; at least I see a lot less of them right after I use it. Sulphur spray is considered an organic product, so you should have no trouble finding it.
Simple; break off a piece, put into watering container and let it sit for one day, then water as usual.
Possible in Bayer 3 in 1 is mixed Bacillus thuringiensis israelensis.
But the problem is; something wrong with media. Fungus gnat thrive when media is too moist for long time, peat moss, slow drainage, etc…