Or does it work only for Whirlpool, Bind, Wrap, etc.?
Iz for moi Lucario. :3
A hold item that causes partially trapping moves to always work for 5 turns.
Source: Bulbapedia/ Grip Claw ___
This is Grip Claw's description. It only works on partially trapping moves ___
Bind Clamp Fire Spin Magma Storm Sand Tomb Whirlpool Wrap
Bulbapdia/ Partially-trapping moves
So no, Bone Rush will not be affected by Grip Claw.
Only for the Moves that actually trap, not associated with Bone Rush. Sorry.