For secular Bible Study, I might recommend Unitarian Universalism, for one. I know several atheists who have invited me to it - to church, and I said, why? What's the point. Apparently, there's some serious investigation from a secular standpoint (including almost every perspective imaginable), which I would enjoy, but as yet I've not bothered since I actually like to not do anything on Sunday morning.
But also, in a more academic sense, since it seems that there are a lot of students on here, religious studies often examines the Bible from a secular standpoint. But for secular Bible study, I'd say check out the first.