This answer falls into multiple categories:
If you're asking about when a book was written or a set of books, or if you're asking about who authored a set of books, it is considered source criticism. This is generally accepted.
- Did Moses write the first five books of the Bible?
- Did Paul write all of the epistles?
If you're asking about where the Bible says one particular thing or another, I think that this is off-topic. These questions, while they seem to be about the Bible, they're actually about doctrine:
- Where does the Bible say that it's OK to beat your wife?
- Where does the Bible say that we shouldn't sin?
A meta post over Christianity.SE explains this more fully.
Unfortunately, there hasn't been any consensus on whether historical questions are on topic.
- How large was the Roman Empire during the time of Jesus?
- Who controlled the land West of Egypt during the time of the Israelites captivity?
This is still an open question, on whether these are on topic: A meta post here about this topic specifically
Some of us think that if a historical question regards helping you understand the text of the Bible, then it's alright. If it doesn't illuminate a specific passage, then it's certainly off topic.
This is a very general category and we have to be careful here. I think this is the specific category about which you are asking. Questions like:
- How many books does the Old Testament have?
- Who determines what books go into the canon?
These questions are, so far, on topic. There hasn't been any movement that I've noticed to have these questions disallowed. However, they have to be specific to the Bible itself.
Be aware that Wikipedia is often the best source of answers for very general questions and it's not in our charter to duplicate Wikipedia. If you ask an overly-broad question, it's likely the best answers will be a summary of the top Google results (including Wikipedia). More focused questions that require expert answers are more appropriate for the site.
Ultimately, questions about the Bible "in general" fall into many categories. Most of these categories are on-topic, but a couple are open questions. Your best bet is to either ask it and see what happens or to ask on Chat whether it's acceptable.
The worst case scenario is that your question will be closed, which isn't so much a death sentence for the question, but a chance to improve the question to meet the site standards. Once the question is more in line with the site, it can be reopened.