From my planning, I guess I can add the following:
Public transport is great for getting to Caen and Bayeux, from there to the beaches is limited, a few buses here and there. I am not the conspiratorial type, but it seems a sight so popular has such a limited public transport option in Europe, just odd.
The region of the landings is lengthy, some 50 miles, so bikes are possible, but not for the entire length easily. You could pick a town to get to, then cycle over a couple days. Since I have not been there yet, I can't say whether the roads support bicycles and cars, or if there are bike racks along the way.
Hitting museums and a couple cemeteries can easily be done on your own. If you know a good amount about the beaches and the invasion, those you can do as well. If you have less background, then most of the beaches are just that, beaches with some bunkers or items on the beach. Stories from a guide may help in that case.
My assessment, I will be renting a car, hitting most of the beaches and museums over two days, might do a tour part of one day, but probably not.