IIRC, the last flight is the CIA (as in Ciampino, not as in "take terrorist suspects to be tortured") flight at 2345, giving a little longer. As this bus is there specifically there to cater to the last few FR flights of the day, then I suspect it will wait a while before leaving.
If it leaves, then, well, your last option is to find some other people heading to Edinburgh (pronounced "Embra" in Ayrshire

) and share a cab. There'll be others in the same boat, and we're a chatty bunch North of the border, so you'll find them easily enough... Either that, or try and find a cheap room - there's a Travelodge in Kilmarnock and a Travel Inn in Ayr.
Just don't expect any assistance from Ryanair if that's the case...