The truth is, we have enough of the old texts that it has been shown that the actual edits in the bible are minor. They do exist, but the core of it is there.
I know you probably know what you mean when you say that but it has the potential to be very misleading. Some naive christian will read that and think you mean that what we have are basically the "very words of God", which of course is not what you said.
You may be referring to the similarities between the dead sea scrolls (dated to something like 300BCE - 50 CE) and the MT (masoretic text, earliest manuscripts around 9th century CE).
Here's what wikipedia has to say:
"The biblical manuscripts from Qumran, which include at least fragments from every book of the Old Testament, except perhaps for the Book of Esther, provide a far older cross section of scriptural tradition than that available to scholars before. While some of the Qumran biblical manuscripts are nearly identical to the Masoretic, or traditional, Hebrew text of the Old Testament, some manuscripts of the books of Exodus and Samuel found in Cave Four exhibit dramatic differences in both language and content. In their astonishing range of textual variants, the Qumran biblical discoveries have prompted scholars to reconsider the once-accepted theories of the development of the modern biblical text from only three manuscript families: of the Masoretic text, of the Hebrew original of the Septuagint, and of the Samaritan Pentateuch. It is now becoming increasingly clear that the Old Testament scripture was extremely fluid until its canonization around A.D. 100"
So we know there were changes. Sometimes "dramatic" changes.
So that's just the OT. What about the NT?
Supposedly written within the latter half of the first century CE. The earliest fragment we have at present is from ~125CE and is the size of a credit card. The earliest complete manuscript is in the 4th century CE. The earliest gospels are I think late 2nd century.
It's worth mentioning that there were no copy machines in those days. Everything was copied by hand. We don't have the original documents, because they have most likely not survived. We don't have the copies, nor the copies of the copies. What we do have is probably well down the line of copies and although we'd like to think we have something close to what was originally written, we have ABSOLUTELY NO WAY TO FIND OUT.
Not only that, but we do have very solid evidence of tampering of other writings by christians, and also a lot of interpolation of writings by competing sects in the early 2nd century.
How reliable is our English Bible today? Here's the real truth, NO ONE KNOWS. We can speculate that it's "fairly accurate" and "well preserved" but there is absolutely no way to be sure. So next time someone talks to you about needing faith, just remember that they first need faith that they're actually reading the right words...