We expected to be able to take a public bus from Bayeux to Arromanches, but the only bus on the day we were there (Thursday) left Bayeux at about noon and left Arromanches about 40 minutes later. We checked with the TI who confirmed that and seemed unaccustomed to checking the public bus schedule. In any case, we were forced to rent a car. My personal expectation is that this is due to private companies wanting control over the bus tours. In the end we were able to spend two or three hours in Arromanches and then drive to Omaha beach and the American Cemetary. Just what we wanted without having to spend the day in a bus and miss the museums we would have wanted to see.
It's a small world after all.
In 2012, when I was in Bayeux, I also rented a car to see the D-Day sites. I always prefer to take public transit whenever possible. (Now I wish I had signed up for an organized tour of D-Day sites.)
I ended up putting 80 miles on the car. I saw the same sites as you as well as Pointe-du-Hoc and the German (and the American) cemetery and the German gun emplacements.
There was one bit of serendipity for me. My dad was a veteran of the US Navy in the Pacific fleet during World War II. At the gun emplacements in Normandy, I met an 88-year-old veteran who also served in the US Navy in the Pacific. I thanked him for his service and told him about my dad.
I'm not sure why you thought there would be tourist friendly public transportation routes and timings to all the various D day associated sites. The public bus is essentially town to town bus routes for locals. Advance research should have shown you that. The usual way for tourists to visit these sites is by renting a car or using a tour or private guide.
The public bus routes are not suppressed for the D Day private tour companies' benefit.
You will find the same thing all over regional France - the public buses are few and far between, and made mostly for schoolchildren and locals.
Nothing to do with collusion between private tour companies and public transportation authorities.
This assumption has gone on for years. Public transportation in rural Normandie is sparse to non existent. I live 25 miles behind the invasion beaches and it would be an all day adventure to get to the American Cemetery at Colleville and only then be able to stay about an hour.
Paris and the other big cities bask in comprehensive transportation networks, while rural areas suffer by comparison. Ultimately exploring the Normandie invasion beaches just begs for a good battlefield guide book and nice car or the services of a guided tour. Every inch of the coast and for miles behind the beaches is brimming with history. Five or six miles from my house is the location of a firefight that resulted in a young British trooper earning a posthumous Victoria Cross.
See Normandie first then follow up with the museum(s). A museum in that area is often just a static display of the accoutrements of war. Perhaps then the best example of reality topping museum displays is the battlefield at Brecourt Manor (Band of Brothers) largely intact. Watch the TV show and then see where it happened!
Seeing/appreciating this area takes some effort that generally is not served up by easy to achieve public transportation connections.
Across from the Bayeux train station or nearby is a bus depot ( gare routiere). The various bus lines stop there The main problem is the frequency of the departures. Most efficiently would be to have a rental car if you want to reach the more remote areas of Normandy connected to 1944. Basically, you need that.