Trying the image again

So the bottom section below the seat is bent in two directions? I'd like to see how that works out.
Single bends: tricky but doable; compound bends: your last name better be Belter or Maloof...
To build-up from laminated layers your 4' radius will be easy, but will require a fully-supportive form (caul) because wood will have harder and softer zones, which will make unsupported bends uneven. Uneven bends are hard to get glued up.
Making the form (caul) takes longer than the bending itself. You should be able to dry-bend 1/4" stuff to a 4' radius. Quartersawn stuff bends the best with least chance of splitting out. Flat sawn is most prone to failure.
Casey

Thanks for the help. I've reconsidered the double bend in the bottom. Do you have any opinion about using MDF and alder veneer for the last layer or going with alder plywood?

Why not use bending luan or wiggleboard then Alder veeer?

I've thought about that, but I'm not sure that those would provide enough structural support for this application. Do you think they would? It sure sounds easier to work with.

No idea I have no idea how far apart the bracing would be. You could possibly run some stiffeners lengthwise.