You can park almost underneith the bridge if they don't close it. From the central square of Bagnoregio (where you can also park if you don't mind the 1.5 km strawl) you drive through the central Via del Corso for 1 km until you pass a church square (Sant Annunziata) on your left. About 400 m down you go right at the big billboard depicting the Civita. Follow the road down to some restaurants just before the bridge. You find a parking almost underneith. Make you go early morning or late afternoon. Enjoy!

There is parking at the end of the town where you take the steps down to the bridge connecting Civita. I noticed cars parked AT the bridge but I have no idea how they got there : there must be a lower road that provides access to that area.

I was there last month - the church is fully open and I don't see any ongoing structural work. Had a brief but interesting conversation with the lady at the souvenir stand inside the church about the whereabouts of the local saint Bonaventure.

I was just there in 2013, and I certainly don't remember seeing any huge indications of renovation such as scaffolding, not being able to enter the church, etc. I don't think there were any areas roped off and entrance certainly wasn't barred. The facade was also completely construction-free, so if there is renovation still, I either wasn't aware of it because I was on cloud nine just being in Civita di Bagnoregio or it just wasn't too horrid looking