If your in a public school located in the US then you can choose not to participate, for private school its another story they play by their own rules. I recommend keeping in mind though its just a book. If you really cant stand it, I recommend going to a higher up in your school system who is not in control of the grade you will receive and ask if you can be transferred to another class. Keep in mind if the teacher you have is the only option that they can greatly effect your grades. If there is only one teacher you can have keep in mind its just a book. Depending on where you are if there are a high number of schools in the area you could transfer to another school system but this might also set you back a bit unless you transfer to an easier one which may ultimately hail hail as genius, you can sometimes still be picked up by bus if it is requirement of yours. When I was was younger I moved around a lot. I also recommend removing yourself from the situation before expressing why you are doing so to avoid negative repercussions. After you are removed from the situations if it matters enough to you, you can try to get media involved this is an extreme example of how far you can take it and your teacher could possibly loose their job. Once again this advise is all for if you are in US public school. There are places I hear of where you would be better advised to take recommendations from others.

I understand trying to exercise your rights to learn about religion in your own way and not have it shoved down your throat. But keep in mind its just a book and everybody is free to interpret it however they want to. So the best course of action is to gain your own interpretation before someone has the chance to force theirs upon you. To avoid a subject matter you don't like or refuse to hear or listen to it can be regarded as ignorance and this is usually not the best course of action, alternatively instead of trying to get out of hearing the reading. You could read up on the subject matter ahead of time take notes and if discussion is allowed politely debate the subject matter. If no discussion of the subject is allowed you could look for ridiculous or conflicting parts of the bible to read to your class. This last bit is probably what I would do essentially turning the bible against itself.

I think if your comfortable with it, you can discuss it with your teacher personally if he is approachable enough for you. :)
Agree that it was not illegal especially if the people there are majority believers. I also think that reading verses or something should not really be harmful not unless you are forced to believe on what you are reading.

I get the impression that many fundamentalist believers think they have found a clever way to get more children exposed to the Bible by pushing for it in public school. In this setting, however, teachers will have less leeway to throw in all the Rube Goldberg theological gymnastics necessary to counter the nonsensical content. It could backfire on them big-time, and I'd just point and laugh.