The bun feet just unscrewed so it was easy to staple the cover onto the bottom and then just screw them back on.
The seams on each corner turned out pretty well too - I just whipped the two edges together with yarn.
This is what it looked like when the hooking was finished, but before I started shaping it to fit the stool.
I'm anxious to give it to her and see if she likes it.
Hmm..... now I'm wondering what my next project will be......