One skein is enough to make one basket (but only in one color). However, since you probably want the handle and rim of the basket to be a different color - why not make two?
Cat Bordhi is my hero! I think she is a knitting genius. These baskets use her Moebius Cast on Method. There are many patterns out there that call themselves a Moebius that actually are not ones. A Moebius has a 180 degree twist with one edge and one side. A Moebius is not interrupted with a seam and is knitted from the middle out.
Have fun with this design. The cat bed I made for Jack uses this technique but without the handle. xo