You didn't indicate how much plastic she ate, or when she ate it. My guess is she is trying to pass it but cannot. You should take her to the vet to make certain her intestines are not blocked. Same way a rawhide chew can affect her. Don't get into the habit of those hide chews. They can be a danger to them. Good luck & send an update.
I use only stainless steel food and water dishes for my dogs and the heavy ceramic dishes for the cats. These last a long time and don't harbor harmful bacteria or give off chemicals like the plastic dishes.
I'm guessing this is a stainless steel bowl that has the black rubber ring around the bottom ...a non-skid bowl? How long ago was it that the dog ate it? I would say time for a trip to the ER vet. She/he could have a blockage.