Hi DH33,
There is more about dust mites in post #2 here but wool has natural properties that can actually help with dust mites because of its ability to control humidity and its lanolin content (see post #9 here) and if you have a mattress protector on top of the wool layer or quilting that prevents skin cells from reaching the wool (which dust mites feed on) then wool wouldn’t be an issue with dust mites.
Bed Bugs are a completely different issue that has nothing to do with the type of mattress you have or the materials inside it (they can infest your home regardless of the type of mattress you have) and if your home is infested with bedbugs then you would need to take measures to eliminate them just like any other pest infestation.
There is also more about mattress protectors (that can also help with dust mites to some degree) in post #89 here and there is more about mattress encasements that can protect against allergens and prevent bed bugs from getting into your mattress (or biting you if they are already inside) in post #2 here.
Phoenix