I train bare footed, I wear sandals, I just assume I'll kick them off before the fight and kick bare footed.
I like the train with bag moving, it's harder to aim if the bag is moving. I even further make it harder to have two bags hanging so I punch and kick one, turn around and do it on the other one, then turn back to the first one. The point is when I go to the second bag, I lost track on how the first one swing. When I turn back to the first one, I would have to acquire the target fast to punch and kick. This is to train for quicker response time and train to be able to hit and different distance instead of the predictable distance.