@Rebecca1635 The fact that the den has a curtain instead of a door is the tricky part, which I imagine is why you were reluctant to list it as a bedroom, as it's true that it doesn't afford much in the way of privacy. For instance, if 2 couples booked the place, they might find it awkward. Is there any way you could put some sort of door there without major renovations? Even a screen, one of those tri-fold things, in addition to the curtain, would make it feel more private, I think.
So I understand the dilemma- you certainly don't want to open yourself up to complaints about falsely advertising it as a bedroom, so I'm not going to say that you should. Maybe some other hosts will weigh in here.
Forget that you've seen air mattresses mentioned in other listings- almost all the advice I've seen from hosts here says not to do it. Air mattresses are fine in our own homes to sleep extra family or friends who come to visit, but in an Airbnb, it seems to convey the idea to guests that the more the merrier. And for you, 4 guests will likely mean the place will tend to be respected- the more guests, generally the bigger the mess and potential for damage. And six people sharing one bathroom may be totally normal in some places in the world, but most first world guests aren't really accustomed to that.
You will likely get requests for more than your max guest count anyway- hosts often do. So you could decide on a case by case basis. If a guest says they are travelling with their spouse and grandma and grandpa but have a child or two, you could decide to give them the use of the air mattress.
I did see that indoor/outdoor seating area, which looks quite nice and could accommodate 6, but the dining table is only suitable for 4, as are the 4 kitchen stools, and the living room area, and if it's raining or something, guests would be hanging out inside.