Headaches with tenant moving out

[Jake Deiters]

Hi BP, just purchased my first duplex (stacked) in St. Louis (South City), inheriting one tenant who is on her way out that I have a couple of questions about. There is no lease in place and she is in the process of moving 4 hours away. She verbally said she'd be out by March 1st. During our rehab of the 1st floor unit we decided it would be best to replace the plumbing stack. Luckily my father in law is a plumber so it's not terrible news. However, this would require us making her bathroom unusable as well. I noticed the tenant upstairs didn't have her boiler on and it's 25 degrees out. I called her, she said we could enter though she wasnt home, and we discovered she had all 4 stove open flames turned on high and she was circulating that heat using a fan! Also had a window cracked and a couple of space heaters going. Couldn't believe it. Anyway, I left her a message saying if she allowed us to demo her bathroom we wouldn't charge rent from then on out. She hasn't been responding. My questions are... 

1. With no lease in place can I demo her bathroom without her permission? She doesn't appear to be "living" there as she's in the process of moving, but still has some stuff there. 

2. How would you go about handling her exit in general with proper notices, delivery confirmation from post office on letter being delivered, etc?

Thanks!