What size of air mattress? And do you care where it's set up?
You could probably fit up to a queen sized air mattress between the edge of the sofa bed and the breakfast bar if you moved the chairs over by the sliding glass door.
My DD is going to use a twin sized air mattress, and I'm planning on putting it in the master next to the king sized bed. She doesn't like sharing a bed, so DS will get the sofa bed and she'll be in the master with me.