I have been running the Bushwacker's recently and if I have no weapons in the arms, is it worth putting armor into them? They don't shield well at all and I rarely lose an arm before a side torso as it stands.
It's not worth it, no. Even with the much better shielding SHD's arms I often just cut it, so especially for barely shielding BSW arms, if you don't use them, don't armor them.