Reading the Bible can be a sin if you are not walking in the Spirit when you do it. In fact, anything that we do that is not in dependence upon Father is sin no matter how good of an action it may appear on the outside, even if that action if reading the perfect word of God.

For example, a non-believer is incapable of pleasing God even if they are reading the Bible because they are in the flesh (Romans 8:8). The non-believer has not been united to the Spirit making it impossible for them to walk in the Spirit leaving all of their actions barren and fruitless.

So what about believers then? Hey great question, thanks for asking! As believers we have a choice to either walk after the flesh or walk in the Spirit. The only thing that can result from flesh is death. In other words fruitlessness (sin). So if your approach to readnig the Bible is fleshly then it is sinful.

How do I know if I am walking after the flesh in regards to reading the Bible? Another great question! Though I can't give you an exhaustive list, I can give an example. If you read your Bible because you feel or think you have to in order to be accepted by God then this is done out of the flesh. We do not have to work for God's acceptance because we already have it in Christ.

Therefore, anything (reading the Bible, any good act, etc.) can be sin if we walk in the flesh. The only way to have works of righteousness is to walk in the Spirit in dependence on Father.