It was fine. I washed it with cold water in my (clean) bathtub with a small amount of woolite. I put a towel on the edge of the tub and laid the dress over it so the bodice is in the water and gently washed it, then did the same thing to rinse it.
The water wicks up, and I was trying to wash as much as possible without getting the print, but some ended up getting into the part with the print, but nothing happened to it either.
If you look on Google there's an old livejournal post about washing puppet circus specifically with a few different opinions. One girl whose opinion I would generally trust says to not wash it or velveteen in general.
However my experience doesn't match this. I have other ap print velveteen pieces that I've washed multiple pieces many times and are fine. I've carefully compared washed waist ties to the unwashed dress, or the matching headbow to the dress after washing it, and I really can't tell any kind of difference.
I'm sure if I were throwing these things in the washing machine and then the dryer they would be fucked up but as it is, washing them in cool water with small amounts of woolite works for me and keep the dresses smelling nice. I only wash them every few wears anyway.