We will be in port at Civitavecchia 7:00h to 17:00h on April 20, 2019. Is there ample time to visit Orvieto and Civita di Bargnorgio using a private/small group tour? Could anyone recommend a private/small group guide/transportation?
You have plenty of time to visit both places. Civitavecchia is 1 hr. 36 min from Orvieto and Orvieto is just 36 min away from Civita di Bargnorgio. Civita di Bargnorgio back to Civitavecchia is only 1 hr. 21 min. So start early in the morning for the trip.
There is plenty to keep you occupied in Orvieto the full day, so from my point of view trying to include Civita di Bagnoregio will cut into Orvieto time. I don't know whether you'll find a guided tour that does both; I'm not at all sure you'll even find a tour just to Orvieto. You may need to arrange something privately, or you could rent a car (something I've never done).
I'd spend the day in Orvieto and not try to see Civita di Bagnoregio.
People have different viewpoints on whether Civita di Bagnoregio is "worth" it or not. Worth is certainly hard to evaluate for someone else but I'm one of the ones that doesn't think the amount of time it takes to get here, walk across the causeway (very high by the way) and see this mostly deserted village is worth it. Others are in alt over it. Here's a recent thread with opinions.
On the other hand, I love Orvieto. It is a wonderful vibrant alive town. The facade of the cathedral is amazing. To me looking at the carvings (especially Eve being birthed from Adam's side) and imagining how an illiterate 14th century believer would have interpreted them is mind-blowing.
Bottom line - to me Civita di Bagnoreggio looks much better in hazy photos from a distance than up close.
I would just stay in Orvieto, so much to see. Getting to Civita takes up a lot of time, getting the bus and walking up the hill. You will spend your day traveling and not seeing much.
Orvieto is amazing. Eat at ristorante de Carlo and drink Orvieto white wine