When you search from any computer is the 'instant book' box checked (or whatever the filter selection is now)? If your place is not 'instant book' and the box is checked, you will not show up.
I feel this is unfair of AirBnB and suspect this was a way to persuade hosts to opt in to 'instant book'. That being said, we have had only positive experiences with instant book. Read about the person and the reviews of and by them. Yopu can learn a lot. AirBnB will let you cancel if you are not happy with the guest.
Of course if the guest hasn't done much on AirBnB with stays or their profile, proceed with caution or message them to learn more about them.