The Evangelical Statement of Faith (1943) begins: "We believe the Bible to be the inspired, the only infallible, authoritative Word of God"
There is no Bible Church nor are there any "Bible Christians" who dispute this. However, Christians who criticize the Roman Church for "not following the Bible", seldom follow the "infallible, authoritative Word of God" themselves when it comes to divorce and remarriage, whereas the Roman Church, at least up until Francis I, has been trying to do so.
I am attending a Christian Missionary Alliance, Bible believing church, and it teaches exactly what Jesus and the rest of His Word teaches regarding divorce.