Well, Elaida would have been killed if she said no, the process is explained in the Companion. Ishmael started the BA when the Aes Sedai began to decline and faith/hope was at a low point. Once it started it was probably pretty easy to find the women who were most predisposed to becoming Black and "nurturing" them before bringing them in. I doubt many women actually sought the Black so much as were identified by the Black as good targets for recruitment. Certainly there were a handful who stumbled upon it, such as Verin, but only Alviarin and Liandrin seem to have been dark friends prior to entering the Tower.

As to the reason the Tower exists I'd disagree that it was about opposing the Dark One, more I'd say it was about survival of mankind. Only the Green Ajah explicitly stands to oppose the Dark One. Brown, Yellow, Gray Blue and Red can all function within their purposes even if the entire Ajah were devoted to the Dark One.