I was thinking I could fake by using 1 x 6's laid flat to create the shaped flat part of the headboard and route the edge of the curve. How do they do the flexible trim on top of the curve?
Yes, this is what I meant by rough cutting on the bandsaw. Trying to rout the shape out of 1x stock will not be easy. Much easier if the router is only doing the final shaping.
For the half round top piece the options which come to my mind are :
a) Assemble from several piece using the 1x6 stock.
b) Steam bend
c) Make a lamination from e.g., 1/8in strips. This thread will give you an idea.
Curved laminated forms
b) and c) will require forms and clamping. b) obviously needs a method to make the steam and a steam box. A lot of work for a one-off.
If the head board is being painted, then the joints from a) or c) would be covered by the paint.
Depending on the radius of the top piece you may need to use thinner strips to allow this to bend without breaking.
FYI, if you go the laminated method and want to use thicker strips like 1/8in, after cutting the strips soak them in water. They will bend a little easier.