Dear dodyskin: I got this from www.word-detective.com :

"Biddy" is actually a very interesting word because it has two separate origins, both fairly well-documented, which is unusual for a slang term. The primary meaning of "biddy" is "chicken," and it first appeared in the early 17th century. The word probably came from the nonsense syllables used to call chickens -- something like "here biddybiddybiddy," I suppose. By the late 18th century "biddy" had been adopted as a derogatory slang term for women, much in the same unfortunate way that "chick" was in the 1960's.

However, "biddy" in this sense might have died a welcome death had it not been for the influx of Irish immigrants into the U.S. in the early 19th century. Young Irish women often had their passage paid by upper-class American families, for whom they would then work as domestic servants while they paid off their debt. The practice was so widespread that such women came to be known as "Biddies," from a shortening of "Bridget," a common Irish women's name. This use of "biddie" reinvigorated theword, and ever since it has been employed by insolent children to torment their elders.