Your atheist friend is wrong. Even non-believing scholars acknowledge that the New Testament was written within a few decades of the Resurrection of Jesus. That's well within living memory, especially when you consider that we were dealing with a mostly illiterate society focused on oral transmission of knowledge.
That's like saying that no one really knows what happened on September 11th 2001, because that's about the span of time involved. Or, say you really want to be difficult about dating; then we're talking about the Sexual Revolution and the early 60s.
It's true that we don't have evidence that anyone wrote anything down at the time of Jesus's ministry, but that's irrelevant. There is a reason he chose twelve disciples (which has the same root word as discipline) and taught them so carefully for 3 1/2 years. Those Apostles not only were thoroughly indoctrinated into Christ's teaching, but they taught others as well. As I said, it was an oral culture, and they knew how to preserve knowledge orally. (One scroll ― they didn't have books ― the size of a Gospel could cost thousands of today's dollars because it had to be hand-written by specialists.)
Jesus died around A.D. 30. The first letter of the New Testament may be dated conservatively to around A.D. 50, and the first Gospel to A.D. 55.
The last book of the Bible to be written, Revelation, is said by some to have been written in A.D. 95 but could have been written in the late A.D. 60s.
Even Wikipedia, which is not exactly a pro-Christian source, says
"Most scholars date Mark [the first Gospel] to c. 66–74 AD, either shortly before or after the destruction of the Second Temple in 70 AD".
(Of John, it says:
"John reached its final form around AD 90–110, although it contains signs of origins dating back to AD 70 and possibly even earlier.")
So tell your atheist friend that Wikipedia says that scholars date the New Testament to no later than 80 years after Jesus's Resurrection, and in some cases within about 35 years, and some scholars date some books within 20 years afterward.
The Bible is a compilation of books penned at different times in different places by various writers.
Most of the Old Testament we don't know who wrote them, though the first five books are traditionally attributed (mostly) to Moses.
The New Testament is clearer. The Gospels are traditionally attributed to
- St. Matthew (an Apostle taught by Jesus)
- St. Mark (a companion of St. Peter the Apostle)
- St. Luke (a companion of St. Paul the Apostle), and
- St. John (an Apostle taught by Jesus).
- St. Luke also wrote the Book of Acts.
- St. Peter wrote two letters (Epistles);
- Three letters and the book of Revelation are attributed to John, but they are not necessarily the same John or the same John that wrote the Gospel.
(There was a John called "the Elder" hanging around who was distinct from St. John, the Apostle).
- St. James, a relative of Jesus, wrote one letter, as did the Apostle St. Jude.
- There is one letter of anonymous origin, Hebrews
The rest of the New Testament is written by St. Paul, an Apostle commissioned by Jesus after His Resurrection.
So as you can see, there is not a lot of distance between Jesus and those who wrote the New Testament.
Some scholars argue for other authorships, in particular claiming that many of these books were not written by Apostles but by communities who followed the Apostles and later wrote in their names. Even if that is true — and I think the claim is dubious and arguable — they were still written in the first century by people devoted to the teachings, not centuries later.
You asked, how has the Bible changed; the answer is, not very much.
Mostly it changed by copyist's error, such as skipping a line, or inserting what was intended as a marginal note, or correcting words that didn't make sense to them. There are a few famous cases where earlier manuscripts lack whole stories, principally I'm thinking of the Woman Caught in Adultery. There is an ending to one of the Gospels (Mark 16:9-20) that does not exist in the earliest manuscripts. But these changes aren't earth-shattering. In general, whenever scholars have discovered ancient manuscripts of the Bible (like the Dead Sea Scrolls) and compared them against what we have today, they are virtually the same.
Remember that the Bible was widely disseminated in a grassroots fashion from the beginning. There was no central authority controlling the Bible content. The New Testament is comprised of 27 books that for centuries circulated independently, most of which started as letters to one church or another. Controlling it would be like trying to control the text of one of those Internet forwards; there are just too many copies in too many hands to alter the content in a malicious and undetectable way.
It's possible your friend is confusing, when the canon of the Bible was finalized with, when it was written. As I said, in the beginning, the 27 books of the New Testament (and the books of the Old Testament) circulated independently, which meant that it wasn't clear exactly to everyone which were inspired and canonical, and which weren't. This sorting process took centuries even though all the books involved were written before about the end of the first century.
Eventually the New Testament canon (list of inspired books) was crystallized around the beginning of the 5th century.
I recommend reading The Bible is a Catholic Book by Jimmy Akin for more information.