That would leave us with a bow that requires a tremendous amount of strength to draw/load, yet one that is also capable of storing a lot of energy
On the contrary. The thing about Adamantine is that it is nearly indestructible but it is VERY VERY fragile.
Or to put it in other terms. Adamantine doesn't bend it just breaks. (Just how Adamantine crafting works has many theories, given that it should be impossible even for the dwarves)
There are a lot of crafts that simply don't work for it and one of those is Bows and crossbows.
If that's the case, then explain adamantine cloth.
Adamantine is, even if what you claim about not bending is true, fragile only in the most technical sense. It is effectively unbreakable by any mortal force. If you had a place to stand and a long, rigid, and slender rod of adamantine, you could move the world. Assuming you used leverage right, of course.
there is no real reason to make a bow out of anything other than wood or composite.
bows are limited by how much force there user can pull(about 200lb tops)
For humans, sure. Dwarves are probably much stronger. Heck, seeing as DF!humans have to battle much more deadly things than RL!humans, even humans might be stronger than humans!