There are a number of tools to read the Bible deeper people learn in seminary of which sometimes clergy forget to share with congregation members. You may very well know this little "tip" in reading the Bible and if so, you are way ahead of the game. If you have not encountered this "tip", I hope this is helpful.
Take a section of the Bible, let us take the story in Matthew 15:21-28.
Step one - look to see if this story is somewhere else in the Bible (this story can be found in Mark 7:25-30)
Step two - look for differences, especially any differences that seems small. (In our case, one of the changes you may notice is the shift of the woman being a Greek-Syrophoenician-woman to a being Cannaite woman.)
Step three - discover where in the Bible we find references to the changes (Cannite's are referenced a number of times in the OT, for instance in Deuteronomy 7:1-6 in which the Cannaite's are one of seven tribes that Israel is "commanded" to conquer with the sword and spear.)
Step four - now you have a point in which to meditate, pray and read and discover a new meaning.
For instance, in this example above you will find that the first encounter the Jewish people had with the Cannaite's made them an enemy to be conquered. When Jesus comes he seeks to reconcile with these people whom have been deemed enemies for generations. Jesus's first encounter with these people, Jesus heals them, feeds them and serves them. Jesus is one who initiates a reconciliation with not only his own people, but also with the long standing enemies of Israel.
So take a look at the Bible and see if these steps are helpful to find new meanings and direction, and see where it takes you.