To get the plywood to bend we'll need steam which means we need a steamer box. Since I have an old kitchen stove in my woodshop I simply drilled out the top of a kettle and installed a hose end in the lid. After adding another hose end to the wooden box, I used a washing machine hose to connect the kettle and the box. This setup gives you tight fittings and is easy to disassemble and store.
The box was made out of plywood scraps and is approximately 6"x12"x48" to accommodate the large plywood pieces needed for the seat. Before putting the box together I drilled a series of holes in the 6" sides for metal rods so the steam would be able to circulate completely around the pieces. The box is open on the end furthest away from where the steam enters the box. Pieces to be steamed are placed in the box through this opening and the opening is covered by a towel during steaming.
With everything assembled, water is brought to a boil and steam is allowed to build up in the box. When steam is rolling out of the box, 2 pieces of 1/8" plywood are placed inside the box and the end covered with a towel. The plywood remains in the steamer for an hour. My experience was more than an hour caused the plywood layers to separate and an hour was long enough to obtain good flexibility.