1. If the Bible were not true, logic would not be meaningful.
Why? The rules of logic precede the bible and many of the oral traditions that eventually came to comprise the bible. The rules of logic are not detailed, or even so-much as mentioned in the bible, and many things described in the bible contradict logic rather than giving it "meaning".
Your argument is flawed in it's very premise by assuming facts not in evidence. You provide no evidence that logic is tied to the bible other than your assertion that it is.
2. Logic is meaningful.
But you provide no evidence or reason as to why the concept of logic would only be "meaningful" if the bible were true. Why is it that cultures across the world, cultures without a tradition in, or even knowledge of, any part of the bible still manage to have a rich and meaningful tradition of logic? Such things should be possible if logic were inexorably tied to the bible.
3. Therefore, the Bible is true.
Anyone could use your flawed and facetious reasoning to claim that any concept is true, and they, like you, would be wrong because your arguement is based on an unproved assertion of facts not in evidence.