You are encountering a circular dependancy: A child bone influences the parent bone, which influences the child bone.
Here's a pseudo explanation of whats going on. Assume, you're moving the mouse in an 45° arc as illustrated on the left. boneB (the child bone) rotates. But since it influences the parent bone slightly, the parent bone will rotate as well. But now the relation of the starting and end position of the mouse towards the shifted origin of the child bone are different and produce another angle. Since the boneB is slightly lower on the right illustration, the angle is slightly bigger, now the parent bone has to be recalculated. And then the child bone, etc. All this happening, while the mouse is being moved obviously produces this weird behaviour.
To solve this problem for the y rotation, simply parent boneB to the parent of boneA. If you wish you can lock the translation axes of boneB.
To create a similiar behaviour for all rotation do the following. (Remember, child bones aren't allowed to influence their parents, if this changing the child bone's properties.)
Create an additional bone, which will be the animated one and parent it to the firstparent (root). Add a copy rotation from the handle to boneB, and a copy rotation constraint to boneA with your desired influence.
The result works, but the handle isn't location at boneB, the segment, which the animator wants to manipulate. This is not intuitive. (At the same time, this is why everything works, the relation of the handle bone to the mouse doesn't change during the rotation operation.)
To enhance the setup, position the handle at a better location. Hide the other bones, or move them to another layer, since the animator doesn't need to touch them. Then choose a custom shape for the handle bone, and choose the boneB in the At field. The custom object will now always be displayed at the position of boneB. The origin of rotation (where the dashed line to the mouse is drawn from), remains at the handle bone's position though.