Hi @Donné1,
It states in this Help Guide, 'once your experience is published on Airbnb, guests can instantly book any dates you’ve made available'. It does therefore imply that there is no option to preapprove guests. If you want to double check this information, however, you can contact Airbnb - this Community Help Guide explains the best ways to contact them (Twitter and Facebook are often best).
Just to let you know, I have moved your post here to a new thread so that it doesn't get lost in another discussion and is easier to find. I have also given it a title, please let me know if you would like to change it!
Kirstie