The second woman to appear in the Bible is...
Eve. Well, according to some scholars, anyway.
Lilith first appears in the Gilgamesh myths of Sumeria (also a big source of the Biblical flood myths) as a demonic entity.
In Genesis 2:22, God creates Eve from Adam's rib. However, in Genesis 1:27, a woman has already been created and according to some scholars, the Talmud, the Book of Enoch, Genesis and an old Jewish folk tale have her as Adam's first wife. She argues that since they were created from the same earth, they are equal. This causes a barney and Lilith says the forbidden name of God and flies off into the air and becomes demonised as a witch. She gets written out, basically.
More conventionally, the second woman mentioned (though she doesn't warrent a name (cos she's female, innit?)) is the wife of Cain. The second woman named is called Adah, wife of Lamech, six generations after Adam.
Never let it be said that the Bible is dismissive of women, eh?