I don't know if Deb is right. Chrysanthemum "bonsai" are only flowerinf herbaceous perennials in pots, but they are a class of bonsai in Japan.
http://www.rep-am.com/articles/2007...tyle/290860.txt
It would seem that if the plant develops a woody stem and isn't an annual, it might qualify as bonsai" material...