For what it's worth, Bible-based religions comprise a minority around the world. Yet most (not all) religions believe in God. So do many philosophies. For example, Aristotle believed in the Prime Mover, i.e., God. He probably never even heard of the Bible (and certainly not of the New Testament since he lived before Christ).
Thus, the belief in God is something totally separate from agreeing or disagreeing with the Bible.
For that matter, at least one noder who is a devout Jew has stated she actively despises certain biblical passages. Yet, she obviously not only believes in God but in the God of the Bible.
It is not all black and white. Nor is it gray. It is a rainbow, and rainbows are beautiful.
Anyway, to answer your question as stated, I actually would not say the Bible is full of things I disagree with. Much of it is simply history. What is there to either agree or disagree with in history? Much of it is spirituality. It is not my spirituality, but that does not give me a reason (let alone right) to disagree with it. There are many spiritual paths. Just because I choose not to walk them does not mean they are no good, or that they do not lead in the right direction.
I am a nontheist: I neither believe in God nor disbelieve. So, I would have to answer, no, I wouldn't start believing in God. It has nothing to do with what I think of the Bible. It is just that the existence or non-existence of God is totally irrelevant to my particular spiritual path (if God does exist, then it is completely beyond my comprehension and anything I might believe about it would be a pointless speculation; if God does not exist, again, what's the point, hence, either way, it is irrelevant to my path).