Quote: *blush!*
White in silkies is almost always recessive, meaning that both parents need to contribute a copy. You will never know if a bird carries one copy or none unless either 1) one of his/her parents was white or 2) one of his/her offspring is white.
If you breed one of Cotton's offspring back to the white, about half the chicks should be white. (I assume that Cotton is the white one
).
Chicken genetics are pretty complicated compared to many other animals, and all the genes carried in a bird go into determining what it looks like. The partridge variety is a specific combination of genes, not just one gene; some are dominant and some are recessive.