I feel you crossed the boundary when you invited her to a meal and with another of your friends as well, it gave her reason to feel more included and perhaps just see herself as a bit more than a guest; what’s done is done and I can fully understanding you were trying to be nice and make the guest feel welcome.
As it stands now, you have got to address this. I would suggest, the next time she is around, make yourself available and give her the opportunity to suggest or refer to anything that seems a bit more personal/ over and aboard the host guest relationship and then politely but firmly draw the line.
To give an example, I'm very friendly, get on easily with people and do enjoy talking to guests the same way I would a neighbour, or friend at the gym, I offer to share my meal if I cook as it’s my culture to do so and after all the are staying in my property, but I do also draw a certain line as this is more of a business deal and we do not really know each other. I had a guest who mistake my friendliness, he returned to the property at the end of his first day out and somehow fell I should be there to welcome him. He entered the property, I could hear from upstairs then he went back to the doorbell and started ringing the to get my attention. He rang me mobile a couple of times and then my landline a couple of times, he send me a message saying he was back home, he gave it 10 mins and repeated the process. I ignored it all, I could tell from the sound of him walking about downstairs, fixing a meal and his phone call in-between that there was no emergency. I eventually when downstairs 35 mins later and I bumped into him, I asked if everything was Ok, he informed me he was just trying to get my attention since he was back home; just as I had suspected! I politely informed him that I was on a conference call and otherwise busy at the time he returned but he has keys and knows were everything he needs is so he does not need to inform me when he gets back to the property. He got the message, it redefined the boundaries and got on well after that, we continued to chat when we did bump into each other but he realised he could not demand my time without good reason.
I do hope she is not booked in for long as what is a concern currently, will soon become an annoyance as well since you feel a bit uncomfortable in your home as well.
There are ways to speak to people directly or indirectly to discuss any concerns which might easily clear any misunderstandings/ unrealistic expectations prior to approaching Airbnb themselves, especially as there is no physical danger involved. She might just be an eccentric person but would feel hurt all the same if you went over her to Airbnb, she does deserve at least one conversation re the situation. However of you do not feel able to handle this approach, then by all means contact Airbnb to express you concern and inform them what exactly you would like them to do, relocate the guest or communicate with her re her manner.
Wish you all the best,
Ama