It's a shame you didn't tackle this, when it first happened, and allowed yourself to be driven from your home.
I would have a friendly chat and let him know that if he wants to stay that is fine but that you took him on, on the basis that he would be out during the day. You need your living space to yourself during the day as you work. Unfortunately him spending time in your working space during the day means you can't do your work effectively.
You appreciate that he wouldn't want to disrupt your work so you have some options to discuss with him if he wants to stay on.....
There are lots of lovely places in your area to visit - mention some indoor and outdoor spaces and places he can go for breakfast, lunch etc
If he does want to spend some time at your house during the day he will need to keep to his room, since you work requires solitutude and concentration.
You can follow this up with a message via BnB so you have this conversation in writing