That's not something the runtime can do, as it doesn't know about you modifying the bone manually based on the mouse position, nor does it know for how long you want to interpolate from the last mouse position to whatever position the bone would have just based on the animation/setup pose.
You'll have to implement this in your user code. When the mouse button/touch is lifted, store the last mouse/touch position. Then, for as long as you want to interpolate, get the current bone position as calculated by the animation/setup pose, interpolate between that and the last mouse/touch position, and finally set the interpolated position on the bone.
