Here's the thing: The Bible is an important piece of literature that has shaped Western Civilization for thousands of years. Even if you don't believe that the stories therein are true, you are at a serious disadvantage, at least as far as cultural awareness in Europe and the Americas, if you don't know these stories.
The Bible used to be taught in schools. There was no reason not to, because pretty much everyone in the schools WERE Christian. No one would be offended. No one questioned it. Even in the US, where there was more diversity, the most controversy you'd get would be whether it was a Catholic Bible or a Protestant one.
As more diverse populations began to immigrate to the US, the US became more pluralistic, and Christianity was no longer the only, or even dominant, religion. Teachers could no longer just assume that everyone in the classroom was a Christian. In fact, more and more, a lot of the teachers were not necessarily Christian. For some reason, administrators thought that meant the Bible had to go.
I'm not sure why they did that.
We learn Greek Mythology in school, even though no one believes in the Greek gods. We read Harry Potter, even though no one believes in Quidditch. As long as the teacher does not try to tell students that they're going to hell if they don't believe it's true, there should be no problem teaching the Bible in school, as it has always been taught.
I suppose I can't speak for others, but when I read the greek myths in school, the teacher didn't have to go out of his way to tell me, "Now, Diva, these are just make believe stories. They're not real." I read them and figured it out all by myself. When I read history books about the Civil War, my teacher didn't have to say, "Okay, now this is real, these aren't just stories, this really did happen." I could tell from context what I was reading and what was intended.
In the same way, I think anyone should be able to read the Bible and figure it out for him- or herself. Teachers don't have to say "this is true" or "this is false." Just read the stories, and let the texts speak to the students as they will.
Either way, these texts need to be taught in school. I don't care if they're taught as fiction or non-fiction, as long as kids learn them. It's sad that two or three generations have grown up now not knowing certain references, like what "30 pieces of silver" means, or what "the shadow of the valley of death" refers to. These are things that are part of our culture, whether you believe in God or not. SHAME on the institution of education for dropping the ball!