Let me preface this by saying that I'm making the implicit assumption that the reader has some typical form of Christian belief (so I don't have to keep saying it).
The Bible, as a piece of literature, was written for people in a specific time and culture.
In that sense, it behooves those who try to understand the Bible to also understand the culture as much as we can, because there is a longstanding (millennia) tradition of reading the text as a vessel of timeless truth—describing God, humanity, and reality—that has eternally important value to the rest of the world (those outside the time/culture of the original audience).
What you say about understanding the culture is important to understanding the message as it was meant to be understood by the original audience. Just because it is imbued with cultural references does not mean that it strictly applies only to that culture, though. Passages that describe God, while cached in the language of some culture, are not truths that change. All truth claims (historical and spiritual) are also timeless and unchanging. Even if the Christian doesn't correctly understand them, that does not negate the true meaning nor does it limit what is intended for the reader to understand.
This understanding of culture is supposed to aid the reader in understanding what God intends for him to know.
Cultural references do not limit the scope of a command.
It seems like the safest assumption on the part of the reader to believe that God means what he says and does not have trouble expressing himself. When God wants to limit the scope of a command, he does so.
Genesis 17:7 (NASB)
"I will establish My covenant between Me and you and your descendants after you..."
Hosea 1:2 (NASB)
the LORD said to Hosea, "Go, take to yourself a wife of harlotry and have children of harlotry..."
God is addressing commands to a certain group of people. It's conceivable that a command could be limited without saying so, but generally, if you look around at the context, it is very clear who such commands are for. To assume that a command is limited unless God says it applies to everyone seems like a risky way to interpret his words.
To briefly address your (hypothetical) examples, for the most important commands, it is usually pretty easy to see the concept addressed from multiple angles and thus arrive at a very reasonable understanding of what is intended.
In the case of premarital sex (or any sort of fornication), here are some different places that provide insight into what is meant by such a prohibition.
- Genesis 39:9 (NASB) How then could I do this great evil and sin against God?
Joseph is rejecting the advances of a married woman.
- Exodus 22:16 and Leviticus 18
prohibitions of sex
- Genesis 2:24 (NASB)
For this reason a man shall leave his father and his mother, and be joined to his wife ; and they shall become one flesh.
the only universal description of what marriage is and its (implied) boundaries
If you look at the command from multiple angles, you get a fairly good idea of what is meant by the prohibition: marriage is meant for a man and a woman married to each other.
Without attempting to address all possible issues, I offer this as a reliable method for understanding what is written so that unstated cultural knowledge doesn't need to be a hindrance (or a worry) to the reader.
What kind of interpretation of the bible lends itself to the Bible being cultural and not intended to be timeless?
Does the Bible mean what I think it means, or does it have a meaning of its own and I need to understand that meaning? For the text not to be timeless, it seems one would have to assume something like the former. To assume that much of the Bible isn't meant to be sufficiently understood as to be useful or that we cannot know what it means is to invalidate it as a reliable source of information. It seems that such an approach would go against any definition of orthodox Christianity and Biblical interpretation.
To answer your other question, I would say that this is a risky exegetical method that a numerical majority of Christians do not employ because it is primarily used by people who don't wish to believe/obey the parts of the text that they do not like.