Note: Ties are pretty difficult to work with. I highly recommend interfacing them, and also being very careful that ties with vertical motifs go straight up the middle of each section instead of running into the strip next to them.
For the bottom, I pieced more ties. I sewed them directly to a circle of fusible fleece. Then I topstitched around the bottom after folding the edge under. I finished with another tie. This one was sewn on not unlike a quilt binding. After I sewed it on (and joined the ends, which is tricky around a curve), I first glued and then hand stitched the finished edge to the bottom of the tuffet.