Whether you like it or not, every Christian who believes in both the Old and New Testaments is a Dispensationalist. If you were not a dispensationalist, you would still be killing and sacrificing animals just like God's people did in the Old Testament.
Sure, Jesus was the Lamb of God that was slain to bear the sins of the World. Under the New Covenant, Jesus did away with the ordinances of old when he instituted his New Covenant with his blood. Is that a new dispensation, or what?
In the millennium, and David speaks of that in the Psalms, sacrificial worship will be resumed (see Ezekiel's temple). Is that a new dispensation or what?
So there you have it. There was the old way of doing business, we are in the new way of doing business, and there is a future way of doing business (yet to come).
"Rightly dividing" the word of God comes up with dispensations. The Bible clearly speaks of the world that was, the world that is, and the world to come.
Do you see it yet? Every Bible Believing Christian is a dispensationalist, like it or not.