Okay, accomodation-wise, you could stay at some nice hotels but there's no cheap hotels around Bagnoregio.
Based yourself in Bagnoregio town & walk to Civita de Bagnoregio...
Sure, you could sleep at the bus stop, I don't think people would give you any problem. Maybe if you are lucky, ask somebody if they could let you sleep on Civita de Bagnoregio ! That would be a great experience indeed !
Better still, just take a day trip to Bagnoregio if you are either in Viterbo (27 km) or Orvieto (19 km). Please make sure you are informed of the times & buses to either, move forward to the next town or backtrack to the town where you based yourself.
The photo shows the door of a house. If you could stay here, count yourself lucky.
It's not easy to get here unless you have your own transport. Nevertheless, it is possible to reach here if you are a lone traveller like me.
The buses from Viterbo & Orvieto commune between them, passing through Bagnoregio. Maybe you have to change a bus or 2 but hey, I said it's not easy didn't I ?
Take the Cotral buses to reach here.