The clasp should extend far enough that you can get the screw out, at least on both of mine they did.
Maybe you can slide the bracelet all the way to the smallest position so you can see why it wont open all the way up .
Be careful taking that spring bars out, at the ends of that are 2 little tiny "shoes" that ride in the track on the clasp and those are a pain in the azz to get fitted back .