At the Boardwalk Bakery, just so you are aware of this, they don't actually take your mug and re-fill it. You show them a mug and they give you your drink in a cup. You then have to transfer from the cup to the mug if you want.
Not bad when you are refilling only one. However, when I went to refill 4, it was a little cumbersome to manage (I was buy myself). From that point on, I brought a Disney bag with me to put the mugs in after I showed them to her and then just carried the drinks myself.