The Mass contains some of the “Bible teaching” involved in Christian development (if you notice, there are readings from usually 4 different books of the Bible at Sunday Mass, and at least 3 on weekdays…and a homily/sermon that follows). But the central focus of the Mass is Christ, not the Bible. We go to Mass to worship God, and hearing His Word is involved in that. Also, if you will read a Missal, the parts of the Mass and the prayers said by the Priest, you will find even more Scripture.
But really, learning the Bible is best done through Bible Study classes. The Church has organizations that put together study guides for Scriptural studies and even for studies on Papal Encyclicals and the Catechism. In this way, we can learn the Faith in the traditional manner, as stated on Eph. You might notice that no where in Scripture does Christ admonish us to study the Bible. In fact, He never once commanded that anything be written down at all…rather we are told by Paul to hold fast to the teachings passed down, whether written or spoken. Through the Church we have those who can help us understand these teachings…but they need not necessarily all be covered during the Mass. Christian life extends and continues outside the Mass.
FWIW, I do think more parishes would do well to have regualr Bible Study during the week or weekends. Catholic catechesis has been poor in many areas the last 50 years or so.