Can we interpret the Bible by finding out what this verse means to me?

Have you ever gone to a Bible study and either they use a curriculum or the Bible itself, and the teacher reads a passage and then opens it up for comments by saying "What does this verse mean to you"? What is happening here is the teacher is confusing interpretation and application. There's a book called Multiply from Multiply Movement, which is David Platt and Francis Chan, written in 2012. Here is an excerpt from link to chapter 9 of their free book-

Know the Difference between Interpretation and Application 

Maybe the most common mistake made in Bible interpretation is when people focus too much on "what this verse means to me." It’s not uncommon for Bible study groups to go around the circle as each person shares an individualized interpretation. Often these interpretations are made with little study and are heavily influenced by opinion and desire. Many times, the various interpretations are incompatible with one another. In this type of setting, the focus is not on what God is saying through the Bible. Instead, each person is focused on what he or she thinks the verse means. Whether it’s clearly articulated or not, this approach reveals the assumption that the Bible has a personalized meaning for each Christian. It might mean one thing to me, but another thing to you.

I'll use an exaggerated example here, by saying, one man might respond by saying 'Yes, this passage says to me that I can sin with impunity." And the other man says, " What it means to me is that I have to follow the Law." Can it be both? No. As with any text, the author had one thing in mind when He wrote it. The fact that there are many different interpretations doesn't mean that we can sow our own agenda into the Bible, come out with different interpretations, and think that that's OK. It isn't.

Sometimes when we talk about "what this passage means to me," we are actually talking about application, rather than interpretation. With interpretation, we are asking what the passage is saying and what it means. With application, we are applying that meaning to our specific situation. Ultimately, each passage has one meaning, but it might have many different applications.

Application depends on our specific life situations, so we may all read the same passage and walk away with different applications. Interpretation, on the other hand, is all about discovering what God has actually said and what He intended to communicate. We should all read the same passage and walk away with the same meaning. Source: Multiply.

The Multiply book is free in pdf format and there are also 24 videos to match each week's lessons.

In the Ligonier online class Principles of Biblical Interpretation, lecturer RC Sproul always says that there is ONE intended meaning for each passage in the Bible. There might be many applications, but the Author intended one meaning. I can give an example of this. In the passages describing the rapture and in the larger context of God's plan for humankind in history, some interpret the rapture to occur before the Day of the LORD, or during the Day of the LORD, or after the Day of the LORD. Since it is one event and it happens only once, there can't be an interpretation of the rapture that includes 'what it means to me' with three different timings.' Only one of those timings is right and the other two are wrong.

John MacArthur at Grace Community Church preached against personal revelation and preached how to interpret the Word properly in this sermon from 2013.

And here is a general lecture on How To Study Your Bible: Interpretation from MacArthur.

Can we understand the one meaning the Author intended? With study, prayer, and the aid of the Holy Spirit, yes. Some passages are admittedly more difficult to understand. Also, we know we can't understand all of the Bible in the same way the LORD does. However let me end with this story I've told and re-told. It fascinates me. Shortly after the Soviet Union fell, John MacArthur was asked by some pastors in the split-off nation of Kazakhstan to come give them a crash course in theology on various topics. The Communist Soviet Union had banned Christianity and when it fell, the secret pastors, new pastors, and new believers needed to get a good foundation in the open. MacArthur came.

At the end of the week, they asked to be taught on eschatology. MacArthur spent 8 hours teaching them from the Bible about last things. At the end of the teaching, they said, "Good. This is what we believe." Having no access to commentaries, external sermons, or other teachings, and relying solely on the Bible, these pastors on one part of the world believed the same thing as another pastor in another part of the world, because they had interpreted rightly and understood the one intended meaning.

Won't it be wonderful when we're there and we all understand the same, and have a strong union in Christ with no error or sin? Meanwhile, in order to reduce the possibility of error, pray fervently and often, study diligently and well, and do not fall for the 'what this verse means to me" claptrap. Stay true to discovering the wonders of the single, intended meaning of the passage you are reading.
Onward and upward!