But continue thou in the things which thou hast learned and hast been assured of, knowing of whom thou hast learned them; And that from a child thou hast known the holy scriptures, which are able to make thee wise unto salvation through faith which is in Christ Jesus. All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness: That the man of God may be perfect, throughly furnished unto all good works.
(2Ti 3:14-17)
Concerning "apostolic Bible study", I find here a basic pattern or possible methodology, or at least a basic set of themes for Bible study.
1. Doctrine. The word properly means "teaching". The Bible is to be studied in order to acquire knowledge, a knowledge of the facts detailed in the Scripture. It would also encompass the "doctrines" or ideology, the "things to be believed", of the Christian faith as revealed in the Bible.
2. Reproof. The word properly means "conviction". The idea is that a person is convinced by a demonstration of evidences or proofs. The Bible is to be studied in order to a) rebuke sin and error (including heresy or false doctrine) and b) demonstrate the correctness of true doctrine. So this would include both polemical theology (ie "apologetics" or correction of false doctrines or errors), systematic and/or Biblical theology (ie the systematic proving of Bible doctrines, likely ascertained in 1 above), as well as the discovery and rebuke of sin and error in the student's life and understanding, if any.
3. Correction. The word properly means "setting something straight or upright". The Bible should be studied for the purpose of setting the student's knowledge, understanding, and life style "right", ie "getting back on the correct path". Correction is the desired result of reproof, which comes from teaching correct information.
4. Instruction in righteousness. The word instruction properly means chastisement, discipline, or pedagogical nurture. In other words, the Bible is to be studied as a means of providing a disciplined training in righteousness. The disciplined training in righteousness is the result of correction, reproof, and teaching.
From this, I see a basic progression, from theoretical to practical. Doctrine and reproof largely deal with the facts and data of Scripture, whereas correction and instruction largely deal with the application and practice of the facts and data of Scripture. So then a basic Bible study framework can be developed which begins with acquiring basic understanding or knowledge of the statements of Scripture, correction of erroneous ideas as well as the proving or "establishing" of correct doctrine(s), leading into a consideration of correcting one's lifestyle, for the purpose of providing a life-long training regimen in following Christ and becoming like Him.
To put this into practice then, a Biblical passage could be looked at in four ways, or to put it another way four layers of Bible study can be applied to a passage:
1. The doctrinal: What does the text SAY? What is the historical, canonical, and doctrinal context of the passage? (When was it written, by whom, to whom, what was going on at the time, why was it written at that time by that person to that audience, etc?) What are the FACTS of the passage? This is a good place for "memorization" by the way.
2. The apologetic and polemical: What errors does this passage correct? How does this passage fit in with other passages on the same topic? How does this passage harmonise with other passages that may seem paradoxical or contradictory? What additional information does this passage provide about other passages? What additional information can other passages provide about this one? What "doctrine(s)" does this passage teach, support, prove, or refute? What errors in the student's thinking, and lifestyle, does this passage rebuke? (This is now transitioning into the next two layers.)
3. The practical corrective: What needs to be changed in the student's faith and praxis (beliefs and practices or actions) as a result of this passage?
4. The disciplinary or pedagogical or training: Whereas layer 3 deals moreso with correcting erroneous thinking, thought processes, and lifestyle choices, and is therefore somewhat "negative", this layer deals with more of the "how to" of how to live properly as a Christian (and thus is the "positive" counterpart to layer 3). Essentially, this deals with the questions of "What do I need to do and how do I do it?"
This is a bare bones outline, it would be productive to flesh each step or layer out a bit more, with some practical suggestions on what makes each step or layer unique and distinct. Or at the least, to keep all four basic layers or aspects in mind when doing any kind of Bible study using some other method. And of the course, the goal is that the student will become "complete/mature and thoroughly equipped for the performance of all good works".