Growing up I had a had a yorkie and he used to do that too. We usually put the garbage on the corner of the countertop to keep him out of it.

Now I have 2 bathrooms. The bathroom off my bedroom I keep the door closed to so the dogs can't get in. The other bathroom I don't use too often, the door stays open, but I just make sure I don't put anything in the garbage that the dogs may have interest in. Doing that I've never had a problem. I don't even know if the dogs would get into it.