I have a concrete block house in SW florida. I have two bump-outs on my house that are wood 2x4 construction with wood t1-11 type siding. The siding is in need of replacement which I could easily do. We get hurricanes here and the wood bumpouts are not very strong. I really don't know why they did that in the 70s-90s. They are literally the only part that rots away and fails these houses. Seems like a stupid compramise... With that being said, I would like to replace them widh ICF with either a 4" or 6" core. My only concern is how do I attach it to the existing concrete block. Also, what ICF block company would you guys suggest? If ICF ends up being a bad idea, I will likely just lay cement block and insulate with 2" foamboard on the inside and stucco the outside. I am hoping to squeeze this project in before the hurricanes come. That way I don't have to be so quick to evacuate.

Does this bump-out have a pad or foundation beneath it? If not, you'll need to pour one.
Likely you will want to dowel into the pad/foundation with rebar to tie the bump-out to the main block wall.

If the shape on the bump-out is somewhat elaborate, you could probably get away with single-sided ICF (leaving concrete exposed on the exterior)..

Your main gotcha is just going to be preventing blowout at the interface with the block wall.
I'd talk with a contractor who is familiar with both concrete block and ICF and ask about tips and tricks for mating the two surfaces.