1/4" plywood only bends well for me when I try to stand it on end.
Drywall will work, but wouldn't be the best choice for a damp location like a shower.. My best results have been with 1/2" plywood scored across the back with a radial arm saw.
When finished, it looks like this;
I doubled it to make a smoother job of it. May not be necessary for tile, but may be necessary for strength, I glued them together and nailed it in place.
A closer view;