Formal:
* Scripture study
* Biblical study
* Scriptural analysis
* Exegesis (in-depth study of a biblical text)
* Hermeneutics (study of biblical interpretation)
Informal:
* Bible reading
* Studying the Word
* Digging into the Scriptures
* Exploring the Bible
* Bible discussion
Other terms:
* Discipleship (a process of learning and growing in faith through the study of the Bible)
* Spiritual formation (a broader term that includes Bible study and other practices)
* Theology (the study of God and religious beliefs)
The best synonym for "Bible study" will depend on the specific context and your intended audience.