I own a Bed & Breakfast. I have just learned that my landlord who was booking stays here (another question) made copies of my key and distributed it to her girlfriends.

If I change my locks, can I charge her for it? Or deduct it from my rent? (which she would oppose as she denies it)

If I change the locks, won't I just have to give her another key, and she can continue to do this?

Once you sign a rental agreement the keys are yours. If your landlord must enter your home at any time, say to check on maintenance, he must have your permission.

You are right, if you changed the locks, you would have to give her a key, but she is crossing the line by giving strangers the key to a rental property you are payng for.

Did she or her g/friends enter your home without asking you permission ? And how did you find out that she has done this ?

Tick

I own and operate a Bed & Breakfast. At the end of a rather bizarre visit, she asked her girlfriends if they had "their key" right in front of me. One said she forgot hers at home, and then left in her car. Later, my landlord insisted she was talking about car keys. Clearly a lie.

As long as she's leasing the space, it's her key to do with as she wishes. Are the keys you're referring to enter a common area? If so, you might have grounds to backcharge. Try replacing your locks with a controlled keyway (such as shclage primus/everest, ASSA, ABLOY or something similar) which she can't get copies of. More expensive to install, but the piece of mind knowing that you control the keys is worth it in my opinion.