Let her gown be tuck'd up to the hips on each side
Shoes too high for to walk or to jump;
And to deck the sweet creature complete for a bride
Let the cork-cutter cut her rump.
London magazine, 1777, Corsets and Crinolines, Norah Waugh
As I haven't found any other documentation for cork rumps than the few mentions in Corsets and Crinolines and those don't tell how they are supposed to be made, this is purely guess work. I started with cork blocks that I carved in shape.
Then I covered them with linen fabric. I made three separate pockets in which to put the cork pieces. I closed the top and added a waist tape. Please excuse the lack of stockings and period footwear.
And finally the skirt shape. It looks a little more pronounced in the picture than in real life.