@Allison458
If you set "availability window" (in section "calender availabiliy") to "dates not available by default", then you listing is published, but will not show up in the search system.
You can sent the direct link to anybody you want:
https://www.airbnb.com/rooms/24136954
If they want to book, open the desired dates on the calender.
Or open 1 date and let them sent an inquiry, to have option to make a special offer
If you want also not to be found outside Airbnb, then disable in your account under "privacy and sharing" the option to be included in search engines.