Religion in and of itself has little to do with spirituality. That's something born inside you and everybody has it whether they realize it or not. Some, like myself, wholeheartedly accept and embrace it while others can't accept it, won't accept it or are completely unaware of it.
In your case, the very structure that was supposed to bring you closer to God has in fact driven you further away. A lot of people feel that way, but I say, the very fact that you continue to take the time to question the Bible and faith in general, demonstrates some level of spirituality. Think about it. If you really had no sense of spirituality, you'd just ignore the Bible and religion altogether and go on your merry way.
Yet, here we are. To me it's obvious that you're still seeking spiritual fulfillment. A need ingrained in you by our creator and something the church has been unable to offer.