Suggest that some of your child’s favourite plastic toys could do with a bath. (This also works as an inducement to head home when you want to but your toddler doesn’t.) Use a sink, bowl, whatever works for your domestic setup. The Child stood on a stool in our ensuite. She also had a plastic apron on, but we only have one because it was a present. Run some warm water, put the plug in the plughole, squirt some washing-up liquid into the sink / bowl. Let the kid go nuts. Yes, the bathroom will get wet and soapy, but then all you have to do is wipe it down and your toddler has now helped to clean the bathroom! BONUS.
Leaving the bathmat on the floor maybe wasn’t so smart, though.