The Bible tells us about the Good News (Gospel) of salvation. The Old Testament tells us of creation, the fall, sin, and God sending the Law and Prophets to show us our need to be restored to us. It tells us of Christ who was to come. The New Testament tells us of His Incarnation, ministry and the economy of our salvation. It contains epistles dealing with specific issues and proclaiming the Gospel. It is not a manual for how to be a Christian, and we insult it if we treat it as such. It is the proclamation of the faith, not a detailed instruction book. God speaks to us through the Bible, but is not the only way He speaks to us. During the 40 days He spent with His Apostles and Disciples between His Resurrection and Ascension, Christ taught them the inner life of the Church that complements the public proclamation of the Bible, including the Liturgy in it's earliest form. After the Holy Spirit came upon them in Pentecost, the Apostles understood all this and went out establishing churches as they were taught. All this did not need to be written down in the Bible, it was and is lived. The proof that the faith and liturgical life of the Orthodox Church is biblical is that it is the only system that fits perfectly with the Bible. Anyone who lives it will see this. Parts of the Bible that just didn't make sense under other systems are revealed in a beautiful unity when looked at from the Orthodox perspective. It can be further proved by any look at history. the Early church was liturgical, and icons used from the beginning. Either Christ failed in that the Church He established went astray right away after He Ascended, or this is how He chose to establish His Church. (obviously the latter)
As for icons, many object on the basis of the OT commandment not to make graven images. But God's instructions for how to make the Tabernacle included the cherubim on the ark, that is, depictions of the heavenly! Archaeology also indicates that there were many more holy images involved in Jewish worship. The commandment was about not worshiping images as God, not against any depictions.
Icons are used liturgically. They are carried in processions, they are venerated (bow before them), the are kissed. This can all seem like too much, like worship. But this is a cultural misunderstanding. If you observe a culture where it is perfectly normal to prostrate before someone if you have offended them, to kiss your parents hands out of respect, etc., suddenly these actions don't look like worship, but normal respect being paid to the icon, and to the saint or event present to us in the icon as would be paid to a parent or any fellow human being.